]>
2017
10
4
ISSN 2008-1898
993
Well-posedness for a class of generalized Zakharov system
Well-posedness for a class of generalized Zakharov system
en
en
In this paper, we study the existence and uniqueness of the global smooth solution for the initial value problem of generalized
Zakharov equations in dimension two. By means of a priori integral estimates and Galerkin method, we first construct the
existence of global solution with some conditions. Furthermore, we prove that the global solution is unique.
1289
1302
Shujun
You
School of Mathematical Sciences
Huaihua University
China
ysj980@aliyun.com
Xiaoqi
Ning
School of Mathematical Sciences
Huaihua University
China
nxq035@163.com
Global solutions
Zakharov equations
well-posedness.
Article.1.pdf
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]
Differential equations for Daehee polynomials and their applications
Differential equations for Daehee polynomials and their applications
en
en
Recently, differential equations for Changhee polynomials and their applications were introduced by Kim et al. and by using
their differential equations, they derived some new identities on Changhee polynomials. Specially, they presented Changhee
polynomials \(Ch_{n+N}(x)\) by sums of lower terms of Changhee polynomials \(Ch_{n}(x)\). Compare to the result, Kim et al. described
Changhee polynomials \(Ch_{n+N}(x)\) via lower term of higher order Chaghee polynomials by using non-linear differential equations
arising from generating function of Changhee polynomials. In the first part of this paper, the author uses the idea of Kim et al.
to apply to generating function for Daehee polynomials. From differential equations associated with the generating function of
those polynomials, we derive some formulae and combinatorial identities.
Also, Kwon et al. developed the method of differential equations from the generating function of Daehee numbers and
investigated new explicit identities of Daehee numbers. In the second part of the present paper, the author applies their methods
to generating function of Daehee polynomials, and get the explicit representations of Daehee polynomials. And specially we
put \(x = 0\) in our results, we can get new representations of Daehee numbers compare to the above results.
1303
1315
Dongkyu
Lim
School of Mathematical Sciences
Nankai University
China
dgrim84@gmail.com
Daehee polynomial
Daehee number
differential equations.
Article.2.pdf
[
[1]
Y.-K. Cho, T. Kim, T. Mansour, S.-H. Rim, On a (r, s)-analogue of Changhee and Daehee numbers and polynomials, Kyungpook Math. J., 55 (2015), 225-232
##[2]
B. S. El-Desouky, A. Mustafa, New results on higher-order Daehee and Bernoulli numbers and polynomials, Adv. Difference Equ., 2016 (2016 ), 1-21
##[3]
T. Kim, Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, J. Number Theory, 132 (2012), 2854-2865
##[4]
T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, Differential equations for Changhee polynomials and their applications, J. Nonlinear Sci. Appl., 9 (2016), 2857-2864
##[5]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976
##[6]
D. S. Kim, T. Kim, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196-208
##[7]
D. S. Kim, T. Kim, Some identities for Bernoulli numbers of the second kind arising from a non-linear differential equation, Bull. Korean Math. Soc., 52 (2015), 2001-2010
##[8]
T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
##[9]
T. Kim, D. S. Kim, T. Komatsu, S.-H. Lee, Higher-order Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials , J. Nonlinear Convex Anal., 16 (2015), 1993-2015
##[10]
H. I. Kwon, T. Kim, J. J. Seo, A note on Daehee numbers arising from differential equations, Glob. J. Pure Appl. Math., 12 (2016), 2349-2354
##[11]
E.-J. Moon, J.-W. Park, S.-H. Rim, A note on the generalized q-Daehee numbers of higher order, Proc. Jangjeon Math. Soc., 17 (2014), 557-565
##[12]
J. J. Seo, S. H. Rim, T. Kim, S. H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc., 17 (2014), 1-9
##[13]
Y. Simsek, Apostol type Daehee numbers and polynomials, Adv. Stud. Contemp. Math., 26 (2016), 555-566
]
A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus
A novel approach for obtaining new identities for the lambda extension of q-Euler polynomials arising from the q-umbral calculus
en
en
In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function.
We make use of such a generalization to derive several properties arising from the q-umbral calculus.
1316
1325
Serkan
Araci
Department of Economics, Faculty of Economics, Administrative and Social Science
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Mehmet
Acikgoz
Department of Mathematics, Faculty of Science and Arts
University of Gaziantep
Turkey
acikgoz@gantep.edu.tr
Toka
Diagana
Department of Mathematics
Howard University
U.S.A
tokadiag@gmail.com
H. M.
Srivastava
Department of Mathematics and Statistics
China Medical University
University of Victoria
Canada
Republic of China
harimsri@math.uvic.ca
\(q\)-Apostol-Euler polynomials
\(q\)-numbers
\(q\)-exponential function
\(q\)-umbral calculus
(\(\lambda،q\))-Euler numbers
(\(\lambda،q\))-Euler polynomials
properties and identities.
Article.3.pdf
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[1]
S. Araci, Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus, Appl. Math. Comput., 233 (2014), 599-607
##[2]
S. Araci, M. Acikgoz, A. Kilicman, Extended p-adic q-invariant integrals on \(\mathbb{Z}_p\) associated with applications of umbral calculus, Adv. Difference Equ., 2013 (2013 ), 1-14
##[3]
S. Araci, M. Acikgoz, E. Sen, On the extended Kim’s p-adic q-deformed fermionic integrals in the p-adic integer ring, J. Number Theory, 133 (2013), 3348-3361
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S. Araci, M. Acikgoz, J. J. Seo, A new family of q-analogue of Genocchi numbers and polynomials of higher order, Kyungpook Math. J., 54 (2014), 131-141
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A. G. Bagdasaryan, An elementary and real approach to values of the Riemann zeta function, Phys. Atom. Nucl., 73 (2010), 251-254
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J.-S. Choi, P. J. Anderson, H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function, Appl. Math. Comput., 199 (2008), 723-737
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J.-S. Choi, P. J. Anderson, H. M. Srivastava, Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions, Appl. Math. Comput., 215 (2009), 1185-1208
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R. Dere, Y. Simsek, H. M. Srivastava, A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra, J. Number Theory, 133 (2013), 3245-3263
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M. E. H. Ismail, M. Rahman, Inverse operators, q-fractional integrals, and q-Bernoulli polynomials, J. Approx. Theory, 114 (2002), 269-307
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T. Kim, q-generalized Euler numbers and polynomials, Russ. J. Math. Phys., 13 (2006), 293-298
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D. S. Kim, T. Kim, q-Bernoulli polynomials and q-umbral calculus, Sci. China Math., 57 (2014), 1867-1874
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D. S. Kim, T. Kim, Some identities of q-Euler polynomials arising from q-umbral calculus, J. Inequal. Appl., 2014 (2014 ), 1-12
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D. S. Kim, T. Kim, Umbral calculus associated with Bernoulli polynomials, J. Number Theory, 147 (2015), 871-882
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D. S. Kim, T. Kim, S.-H. Lee, J.-J. Seo, A note on q-Frobenius-Euler numbers and polynomials, Adv. Studies Theor. Phys., 7 (2013), 881-889
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T. Kim, T. Mansour, S.-H. Rim, S.-H. Lee, Apostol-Euler polynomials arising from umbral calculus, Adv. Difference Equ., 2013 (2013 ), 1-7
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B. A. Kupershmidt, Reflection symmetries of q-Bernoulli polynomials, J. Nonlinear Math. Phys., 12 (2005), 412-422
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Q.-M. Luo, The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Transforms Spec. Funct., 20 (2008), 377-391
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N. I. Mahmudov, On a class of q-Bernoulli and q-Euler polynomials, Adv. Difference Equ., 2013 (2013), 1-11
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N. I. Mahmudov, M. E. Keleshteri, On a class of generalized q-Bernoulli and q-Euler polynomials, Adv. Difference Equ., 2013 (2013 ), 1-10
##[21]
Á . Pintér, H. M. Srivastava, Addition theorems for the Appell polynomials and the associated classes of polynomial expansions, Aequationes Math., 85 (2013), 483-495
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S.-H. Rim, J.-H. Jeong, On the modified q-Euler numbers of higher order with weight, Adv. Stud. Contemp. Math. (Kyungshang), 22 (2012), 93-98
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E. Sen, Theorems on Apostol-Euler polynomials of higher order arising from Euler basis, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 337-345
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H. M. Srivastava,/ , Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5 (2011), 390-444
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H. M. Srivastava, J.-S. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier, Inc., Amsterdam (2012)
]
Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces
Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces
en
en
Based on a specific way of choosing the indices and a new concept, namely, an analogue of inner product, a modified
Krasnoselski-Mann iteration scheme is proposed for approximating common fixed points of a countable family of asymptotically
nonexpansive mappings; and a strong convergence theorem is established in the framework of CAT(0) spaces. Our results greatly
improve and extend those of the authors whose related researches just involve a single mapping and the weaker \(\Delta\)-convergence.
1326
1333
Shanguang
Qian
Architectural Engineering Faculty
Kunming Metallurgy College
P. R. China
qiansg1975@126.com
Wei-Qi
Deng
School of Statistics and Mathematics
Yunnan University of Finance and Economics
P. R. China
dwq1273@126.com
Krasnoselski-Mann iteration
CAT(0) spaces
infinite families of nonexpansive mappings
strong convergence
\(\Delta\)-convergence.
Article.4.pdf
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W.-Q. Deng, P. Bai, An implicit iteration process for common fixed points of two infinite families of asymptotically nonexpansive mappings in Banach spaces, J. Appl. Math., 2013 (2013 ), 1-6
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S. Dhompongsa, W. Fupinwong, A. Kaewkhao, Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces, Nonlinear Anal., 70 (2009), 4268-4273
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S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45
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S. Dhompongsa, W. A. Kirk, B. Sims, Fixed points of uniformly Lipschitzian mappings, Nonlinear Anal., 65 (2006), 762-772
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W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees , Fixed Point Theory Appl., 2004 (2004), 1-8
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W. A. Kirk, Geodesic geometry and fixed point theory, II, International Conference on Fixed Point Theory and Applications Yokohama Publ., Yokohama, (2004), 113-142
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W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), 3689-3696
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L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl., 325 (2007), 386-399
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T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60 (1976), 179-182
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B. Nanjaras, B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 2010 (2010), 1-14
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M. O. Osilike, S. C. Aniagbosor, B. G. Akuchu, Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, PanAmer. Math. J., 12 (2002), 77-88
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S. Saejung, Halpern’s iteration in CAT(0) spaces, Fixed Point Theory Appl., 2010 (2010), 1-13
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N. Shahzad, Fixed point results for multimaps in CAT(0) spaces, Topology Appl., 156 (2009), 997-1001
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N. Shahzad, Invariant approximations in CAT(0) spaces, Nonlinear Anal., 70 (2009), 4338-4340
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N. Shahzad, J. Markin, Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces, J. Math. Anal. Appl., 337 (2008), 1457-1464
]
Topological structures and the coincidence point of two mappings in cone b-metric spaces
Topological structures and the coincidence point of two mappings in cone b-metric spaces
en
en
Let (X, d,K) be a cone b-metric space over a ordered Banach space (\(E,\preceq\)) with respect to cone P. In this paper, we study
two problems:
(1) We introduce a b-metric \(\rho_c\) and we prove that the b-metric space induced by b-metric \(\rho_c\) has the same topological
structures with the cone b-metric space.
(2) We prove the existence of the coincidence point of two mappings \(T , f : X \rightarrow X\) satisfying a new quasi-contraction of the
type \(d(Tx, Ty) \preceq \Lambda\{d(fx, fy), d(fx, Ty), d(fx, Tx), d(fy, Ty), d(fy, Tx)\}\), where \(\Lambda : E \rightarrow E\) is a linear positive operator and
the spectral radius of \(K\Lambda\) is less than 1.
Our results are new and extend the recent results of [N. Hussain, M. H. Shah, Comput. Math. Appl., 62 (2011), 1677–1684], [M.
Cvetković, V. Rakočević, Appl. Math. Comput., 237 (2014), 712–722], [Z. Kadelburg, S. Radenović, J. Nonlinear Sci. Appl., 3
(2010), 193–202].
1334
1344
Congjun
Zhang
School of Applied Mathematics
Nanjing University of Finance and Economics
China
zcjyysxx@163.com
Sai
Li
School of Applied Mathematics
Nanjing University of Finance and Economics
China
13873030596@163.com
Baoqing
Liu
School of Applied Mathematics
Nanjing University of Finance and Economics
China
liubaoqing1023@sina.com
Topological structures
cone b-metric spaces
quasi-contraction
points of coincidence
common fixed points.
Article.5.pdf
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[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
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C. D. Aliprantis, R. Tourky, Cones and duality, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2007)
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H. Çakallı, A. Sönmez, Ç . Genç, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25 (2012), 429-433
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M. Cvetković, V. Rakočević, Quasi-contraction of Perov type, Appl. Math. Comput., 237 (2014), 712-722
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S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276
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L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
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J. Jachymski, J. Klima, Cantor’s intersection theorem for K-metric spaces with a solid cone and a contraction principle, J. Fixed Point Theory Appl., 18 (2016), 445-463
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G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261-263
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Z. Kadelburg, S. Radenović, Some common fixed point results in non-normal cone metric spaces, J. Nonlinear Sci. Appl., 3 (2010), 193-202
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M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129
##[12]
G.-X. Song, X.-Y. Sun, Y. Zhao, G.-T. Wang, New common fixed point theorems for maps on cone metric spaces, Appl. Math. Lett., 23 (2010), 1033-1037
]
Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers
en
en
In the paper, the authors find a simple and significant expression in terms of the Stirling numbers for derivative polynomials
of a function with a parameter related to the higher order Apostol-Euler numbers and to the higher order Frobenius-Euler
numbers. Moreover, the authors also present a common solution to a sequence of nonlinear ordinary differential equations.
1345
1349
Jiao-Lian
Zhao
Department of Mathematics and Physics
Weinan Normal University
China
zhaojl2004@gmail.com
Jing-Lin
Wang
Department of Mathematics, College of Science
Tianjin Polytechnic University
China
jing-lin.wang@hotmail.com
Feng
Qi
Department of Mathematics, College of Science
Institute of Mathematics
Tianjin Polytechnic University
Henan Polytechnic University
China
China
qifeng618@msn.com
Derivative polynomial
Stirling number
nonlinear ordinary differential equation
solution.
Article.6.pdf
[
[1]
B.-N. Guo, F. Qi, Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind, J. Comput. Appl. Math., 272 (2014), 251-257
##[2]
B.-N. Guo, F. Qi, Some identities and an explicit formula for Bernoulli and Stirling numbers, J. Comput. Appl. Math., 255 (2014), 568-579
##[3]
M. E. Hoffman, Derivative polynomials for tangent and secant, Amer. Math. Monthly, 102 (1995), 23-30
##[4]
T. Kim, G.-W. Jang, J. J. Seo, Revisit of identities for Apostol-Euler and Frobenius-Euler numbers arising from differential equation, J. Nonlinear Sci. Appl., 10 (2017), 186-191
##[5]
T. Kim, D. S. Kim, Some identities of Eulerian polynomials arising from nonlinear differential equations, Iran. J. Sci. Technol. Trans. A Sci., 2016 (2016 ), 1-6
##[6]
T. Kim, D. S. Kim, Differential equations associated with Catalan–Daehee numbers and their applications, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 111 (2017), 1-11
##[7]
T. Kim, D. S. Kim, L.-C. Jang, H. I. Kwon, On differential equations associated with squared Hermite polynomials, J. Comput. Anal. Appl., 23 (2017), 1252-1264
##[8]
T. Kim, D. S. Kim, J.-J. Seo, D. V. Dolgy, Some identities of Chebyshev polynomials arising from non-linear differential equations, J. Comput. Anal. Appl., 23 (2017), 820-832
##[9]
F. Qi, Derivatives of tangent function and tangent numbers, Appl. Math. Comput., 268 (2015), 844-858
##[10]
F. Qi, Explicit formulas for the convolved Fibonacci numbers, ResearchGate Working Paper, (2016), 1-9
##[11]
F. Qi, B.-N. Guo, Explicit formulas and nonlinear ODEs of generating functions for Eulerian polynomials, ResearchGate Working Paper, (2016), 1-5
##[12]
F. Qi, B.-N. Guo, Some properties of a solution to a family of inhomogeneous linear ordinary differential equations, Preprints, 2016 (2016), 1-11
##[13]
F. Qi, B.-N. Guo, Some properties of the Hermite polynomials and their squares and generating functions, Preprints, 2016 (2016), 1-14
##[14]
F. Qi, B.-N. Guo, Viewing some nonlinear ODEs and their solutions from the angle of derivative polynomials, ResearchGate Working Paper, (2016), 1-10
##[15]
F. Qi, B.-N. Guo, Viewing some ordinary differential equations from the angle of derivative polynomials, Preprints, 2016 (2016), 1-12
##[16]
F. Qi, J.-L. Zhao, The Bell polynomials and a sequence of polynomials applied to differential equations, Preprints, 2016 (2016 ), 1-8
##[17]
F. Qi, J.-L. Zhao, Some properties of the Bernoulli numbers of the second kind and their generating function, J. Differ. Equ. Appl., (2017), -
##[18]
C.-F. Wei, B.-N. Guo, Complete monotonicity of functions connected with the exponential function and derivatives, Abstr. Appl. Anal., 2014 (2014), 1-5
##[19]
A.-M. Xu, Z.-D. Cen, Some identities involving exponential functions and Stirling numbers and applications, J. Comput. Appl. Math.,, 260 (2014), 201-207
##[20]
A.-M. Xu, Z.-D. Cen, Closed formulas for computing higher-order derivatives of functions involving exponential functions, Appl. Math. Comput., 270 (2015), 136-141
##[21]
J.-L. Zhao, J.-L. Wang, F. Qi, Derivative polynomials of a function related to the Apostol–Euler and Frobenius–Euler numbers, ResearchGate Working Paper, (2017), 1-5
]
Fixed point theorems for contractive mappings and Ćirić-Maiti-Pal orbit mappings of contractive type in re-defined generalized metric spaces
Fixed point theorems for contractive mappings and Ćirić-Maiti-Pal orbit mappings of contractive type in re-defined generalized metric spaces
en
en
In this paper, the re-defined generalized metric space which is equivalent to the generalized metric spaces defined by Jleli
and Samet is presented so that some well-known spaces are incorporated in the area of re-defined generalized metric spaces.
Some fixed point existence and uniqueness results of contractive and generalized contraction mappings defined on such metric
spaces are provided. Especially, we discussed the fixed point existence results of Ćirić-Maiti-Pal orbit mappings of contractive
type in the re-defined generalized metric spaces. In addition, some examples are provided to better support the fixed point
results.
1350
1364
Xiaoming
Fan
College of Teacher Education
Harbin Normal University
P. R. China
fanxm093@163.com
Zhigang
Wang
School of Mathematical Sciences
Harbin Normal University
P. R. China
wangzg2003205@163.com
Re-defined generalized metric space
fixed point theorems
Ćirić-Maiti-Pal orbit mapping of contractive type
f-orbitally complete.
Article.7.pdf
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N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012 ), 1-12
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M. Jleli, B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., 2015 (2015 ), 1-14
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J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212
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]
Carathéodory's approximate solution to stochastic differential delay equation
Carathéodory's approximate solution to stochastic differential delay equation
en
en
In this paper, we show the difference between an approximate solution and an accurate solution for a stochastic differential
delay equation, where the approximate solution, which is called by Carathéodory, is constructed by successive approximation.
Furthermore, we study the p-th moment continuity of the approximate solution for this delay equation.
1365
1376
Yeol Je
Cho
Department of Mathematics Education and the RINS
Center for General Education
Gyeongsang National University
China Medical University
Republic of Korea
Taiwan
yjcho@gnu.ac.kr
Young-Ho
Kim
Department of Mathematics
Changwon National University
Republic of Korea
yhkim@changwon.ac.kr
Hölder’s inequality
moment inequality
Carathéodory approximation procedure
stochastic differential delay equation.
Article.8.pdf
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[1]
Y. J. Cho, S. S. Dragomir, Y.-H. Kim, A note on the existence and uniqueness of the solutions to SFDES, J. Inequal. Appl., 2012 (2012 ), 1-11
##[2]
S. Janković, G. Pavlović, Moment decay rates of stochastic differential equations with time-varying delay, Filomat, 24 (2010), 115-132
##[3]
Y.-H. Kim, A note on the solutions of neutral SFDEs with infinite delay, J. Inequal. Appl., 2013 (2013 ), 1-11
##[4]
Y.-H. Kim, The difference between the approximate and the accurate solution to stochastic differential delay equation, Proc. Jangjeon Math. Soc., 18 (2015), 165-175
##[5]
X.-R. Mao, Stochastic differential equations and applications, Second edition, Horwood Publishing Limited, Chichester (2008)
##[6]
M. Milošević, On the approximations of solutions to stochastic differential delay equations with Poisson random measure via Taylor series, Filomat, 27 (2013), 201-214
##[7]
Y. Ren, S.-P. Lu, N.-M. Xia, Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math., 220 (2008), 364-372
##[8]
Y. Ren, N.-M. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput., 210 (2009), 72-79
##[9]
M. Vasilova, M. Jovanović, Dynamics of Gilpin-Ayala competition model with random perturbation, Filomat, 24 (2010), 101-113
##[10]
F.-Y.Wei, Y.-H. Cai, Existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay under non-Lipschitz conditions, Adv. Difference Equ., 2013 (2013), 1-12
##[11]
F.-Y. Wei, K. Wang, The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl., 331 (2007), 516-531
]
Fixed point results for generalized contractive mappings involving altering distance functions on complete quasi-metric spaces and applications
Fixed point results for generalized contractive mappings involving altering distance functions on complete quasi-metric spaces and applications
en
en
In this paper, we introduce \(\alpha-\psi-\phi\)-Jachymski contractive mappings with generalized altering distance functions in the
setting of quasi-metric spaces. Some theorems on the existence and uniqueness of fixed points for such mappings via admissible
mappings are established. Utilizing above abstract results, we derive common fixed point theorem for two operators and
multidimensional fixed point results for nonlinear mappings satisfying different kinds of contractive conditions on partially
ordered metric spaces. Moreover, we present some examples and applications in a Fredholm integral equation and an initial
value problem for partial differential equation of parabolic type.
1377
1398
Yanbin
Sang
School of Science
North University of China
China
syb6662004@163.com
Admissible mapping
altering distance
multidimensional
w-distance
partial order.
Article.9.pdf
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[1]
C. Alegre, J. Marín, S. Romaguera, A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-8
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H. H. Alsulami, S. Gülyaz I. M. Erhan, Fixed points of \(\alpha\)-admissible Meir-Keeler contraction mappings on quasi-metric spaces, J. Inequal. Appl., 2015 (2015 ), 1-15
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H. H. Alsulami, S. Gülyaz , E. Karapınar, ˙I. M. Erhan, Fixed point theorems for a class of \(\alpha\)-admissible contractions and applications to boundary value problem, Abstr. Appl. Anal., 2014 (2014 ), 1-10
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V. Berinde, Coupled fixed point theorems for \(\phi\)-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 75 (2012), 3218-3228
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M. Borcut, V. Berinde, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 5929-5936
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P. Chaipunya, Y. J. Cho, P. Kumam, Geraghty-type theorems in modular metric spaces with an application to partial differential equation, Adv. Difference Equ., 2012 (2012 ), 1-12
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R. H. Haghi, S. Rezapour, N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799-1803
##[9]
J. Jachymski, Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 194 (1995), 293-303
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E. Karapınar, I . M. Erhan, A. Öztürk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 57 (2013), 2442-2448
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E. Karapınar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013 ), 1-12
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H. Lakzian, D. Gopal, W. Sintunavarat, New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations, J. Fixed Point Theory Appl., 18 (2016), 251-266
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V. La Rosa, P. Vetro, Common fixed points for \(\alpha-\psi-\phi\)-contractions in generalized metric spaces, Nonlinear Anal. Model. Control, 19 (2014), 43-54
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X.-L. Liu, A. H. Ansari, S. Chandok, C.-K. Park, Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions, J. Nonlinear Sci. Appl., 9 (2016), 1564-1580
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N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal., 74 (2011), 983-992
##[17]
J. Marín, S. Romaguera, P. Tirado, Generalized contractive set-valued maps on complete preordered quasi-metric spaces, J. Funct. Spaces Appl., 2013 (2013 ), 1-6
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A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), 326-329
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S. Park, On generalizations of the Ekeland-type variational principles, Nonlinear Anal., 39 (2000), 881-889
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P. D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal., 64 (2006), 546-557
##[21]
A. Roldán, J. Martínez-Moreno, C. Roldán, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl., 396 (2012), 536-545
##[22]
A. Roldán, J. Martínez-Moreno, C. Roldán, Y. J. Cho, Multidimensional fixed point theorems under ( \(\psi,\phi\))-contractive conditions in partially ordered complete metric spaces, J. Comput. Appl. Math., 273 (2015), 76-87
##[23]
A. Roldán, J. Martínez-Moreno, C. Roldán, E. Karapınar, Some remarks on multidimensional fixed point theorems, Fixed Point Theory, 15 (2014), 545-558
##[24]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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Y.-B. Sang, Q. Meng, Fixed point theorems with generalized altering distance functions in partially ordered metric spaces via w-distances and applications, Fixed Point Theory Appl., 2015 (2015), 1-25
##[26]
T. Suzuki, Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci., 2007 (2007), 1-6
]
On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
On the generalized Ulam-Hyers-Rassias stability for quartic functional equation in modular spaces
en
en
In this paper, we prove the generalized UHR stability of a quartic functional equations f(2x + y) + f(2x - y) = 4f(x + y) +
4f(x - y) + 24f(x) - 6f(y) via the extensive studies of fixed point theory. Our results are obtained in the framework of modular
spaces by the modular which is l.s.c. and convex.
1399
1406
Kittipong
Wongkum
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
Thailand
Thailand
kittipong.wong@mail.kmutt.ac.th
Poom
Kumam
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
Department of Medical Research, China Medical University Hospital
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Yeol Je
Cho
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
Department of Mathematics Education
King Mongkut’s University of Technology Thonburi (KMUTT)
Gyeongsang Natoinal University
Thailand
Korea
yjcho@gnu.ac.kr;yjchomath@gmail.com
Phatiphat
Thounthong
Renewable Energy Research Centre
Department of Teacher Training in Electrical Engineering, Faculty of Technical Education
King Mongkuts University of Technology North Bangkok (KMUTNB)
King Mongkuts University of Technology North Bangkok (KMUTNB)
Thailand
Thailand
phtt@kmutnb.ac.th
Parin
Chaipunya
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
Thailand
Thailand
parin.cha@mail.kmutt.ac.th
Quartic mapping
generalized UHR stability
modular space.
Article.10.pdf
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T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
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Y. J. Cho, C.-K. Park, T. M. Rassias, R. Saadati, Stability of functional equations in Banach algebras, Springer, Cham (2015)
##[3]
Y. J. Cho, T. M. Rassias, R. Saadati, Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, Springer, New York (2013)
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D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224
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M. A. Khamsi, Quasicontraction mappings in modular spaces without \(\Delta_2\)-condition, Fixed Point Theory Appl., 2008 (2008), 1-6
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Y.-S. Lee, S.-Y. Chung, Stability of quartic functional equations in the spaces of generalized functions, Adv. Difference Equ., 2009 (2009), 1-16
##[7]
S. H. Lee, S. M. Im, I. S. Hwang, Quartic functional equations, J. Math. Anal. Appl., 307 (2005), 387-394
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T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
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J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. III, 34(54) (1999), 243-252
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S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York (1964)
]
Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces
Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces
en
en
In this paper, we introduce and study a class of new modified iterative approximation processes for two finite families of
total asymptotically nonexpansive nonself mappings in hyperbolic spaces. By using generalization of Schu’s lemma and Tan-Xu’s
inequality, some important related properties of this modified iterative approximation are proposed and analyzed. Further, based
on the related properties, we prove \(\Delta\)-convergence and strong convergence of the modified iterative approximating process in
hyperbolic spaces. Because a total asymptotically nonexpansive nonself mapping in hyperbolic spaces includes asymptotically
nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0)
spaces as special cases, the results presented in this paper improve and generalize the corresponding results in the literature.
1407
1423
Ting-jian
Xiong
Department of Mathematics
Sichuan University of Science & Engineering
P. R. China
Heng-you
Lan
Department of Mathematics
Sichuan University of Science & Engineering
P. R. China
hengyoulan@163.com
Convergence analysis
new modified iterative approximating process
\(\Delta\)-convergence and strong convergence
total asymptotically nonexpansive nonself mapping
hyperbolic space.
Article.11.pdf
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[1]
R. P. Agarwal, D. O’Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear convex Anal., 8 (2007), 61-79
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B. Ali, Convergence theorems for finite families of total asymptotically nonexpansive mappings in hyperbolic spaces, Fixed Point Theory Appl., 2016 (2016 ), 1-13
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M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (1999)
##[4]
H. Fukhar-ud-din, M. A. A. Khan, Convergence analysis of a general iteration schema of nonlinear mappings in hyperbolic spaces, Fixed Point Theory Appl., 2013 (2013), 1-18
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S.H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory Appl., 2013 (2013 ), 1-10
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S. H. Khan, H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 61 (2005), 1295-1301
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A. R. Khan, H. Fukhar-ud-din, M. A. A. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl., 2012 (2012 ), 1-12
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A. R. Khan, M. A. Khamsi, H. Fukhar-ud-din, Strong convergence of a general iteration scheme in CAT(0) spaces, Nonlinear Anal., 74 (2011), 783-791
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U. Kohlenbach, Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc., 357 (2005), 89-128
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W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), 3689-3696
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P. K. F. Kuhfittig, Common fixed points of nonexpansive mappings by iteration, Pacific J. Math., 97 (1981), 137-139
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P. Kumam, G. S. Saluja, H. K. Nashine, Convergence of modified S-iteration process for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces, J. Inequal. Appl., 2014 (2014 ), 1-15
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L. Leuştean, Nonexpansive iterations in uniformly convex W-hyperbolic spaces, Nonlinear analysis and optimization I,/ Nonlinear analysis, Contemp. Math., Israel Math. Conf. Proc., Amer. Math. Soc., Providence, RI, 513 (2010), 193-209
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Y. Li, L. H. Bo, \(\Delta\)-convergence analysis of improved Kuhfittig iterative for asymptotically nonexpansive nonself-mappings in W-hyperbolic spaces, J. Inequal. Appl., 2014 (2014 ), 1-9
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T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60 (1976), 179-182
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M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229
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S. Plubtieng, K. Ungchittrakool, R. Wangkeeree, Implicit iterations of two finite families for nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim., 28 (2007), 737-749
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S. Reich, I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal., 15 (1990), 537-558
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A. Şahin, M. Başarır, On the strong and \(\Delta\)-convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 2013 (2013 ), 1-10
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A. Şahin, M. Başarır, Some convergence results for modified SP-iteration scheme in hyperbolic spaces, Fixed Point Theory Appl., 2014 (2014 ), 1-11
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J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153-159
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H. F. Senter, W. G. Dotson Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44 (1974), 375-380
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B. S. Thakur, D. Thakur, M. Postolache, Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015 ), 1-11
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L.-L. Wan, \(\Delta\)-convergence for mixed-type total asymptotically nonexpansive mappings in hyperbolic spaces, J. Inequal. Appl., 2013 (2013), 1-8
##[29]
L.-L. Wan, Demiclosed principle and convergence theorems for total asymptotically nonexpansive nonself mappings in hyperbolic spaces, Fixed Point Theory Appl., 2015 (2015 ), 1-10
##[30]
L.Wang, S.-S. Chang, Z.-L. Ma, Convergence theorems for total asymptotically nonexpansive non-self mappings in CAT(0) spaces, J. Inequal. Appl., 2013 (2013 ), 1-10
##[31]
T.-J. Xiong, H.-Y. Lan, Convergence analysis of new iterative approximating schemes with errors for total asymptotically nonexpansive mappings in hyperbolic spaces, J. Comput. Anal. Appl., 20 (2016), 902-913
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L. Yang, F. H. Zhao, Strong and \(\Delta\)-convergence theorems for total asymptotically nonexpansive nonself mappings in CAT(0) spaces, J. Inequal. Appl., 2013 (2013 ), 1-17
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I. Yildirim, M. Özdemir, Approximating common fixed points of asymptotically quasi-nonexpansive mappings by a new iterative process, Arab. J. Sci. Eng., 36 (2011), 393-403
]
Some fixed point theorems for contractive mapping in ordered vector metric spaces
Some fixed point theorems for contractive mapping in ordered vector metric spaces
en
en
In this paper, considering an order relation on a vector metric space which is introduced by Çevik and Altun in 2009, we
present some fundamental fixed point results. Then, we provide some nontrivial examples show that the investigation of this
work is significant.
1424
1432
Cüneyt
Çevik
Department of Mathematics, Faculty of Science
Gazi University
Turkey
ccevik@gazi.edu.tr
Ishak
Altun
Department of Mathematics, College of Science
Department of Mathematics, Faculty of Science
King Saud University
Kırıkkale University
Saudi Arabia
Turkey
ishakaltun@yahoo.com
Hakan
Şahin
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
Gazi University
Amasya University
Turkey
Turkey
hakansahin@gazi.edu.tr
Çetin Cemal
Özeken
Department of Mathematics, Faculty of Science
Gazi University
Turkey
cetinozeken@gazi.edu.tr
Fixed point
Riesz space
vector metric space.
Article.12.pdf
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C. D. Aliprantis, K. C. Border, Infinite dimensional analysis: A hitchhiker’s guide, Springer-Verlag, Berlin (1999)
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C. Çevik, On continuity of functions between vector metric spaces, J. Funct. Space, 2014 (2014 ), 1-6
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C. Çevik, I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34 (2009), 375-382
##[4]
N. Hussain, C. Vetro, F. Vetro, Fixed point results for \(\alpha\)-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362-378
##[5]
P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013 ), 1-9
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W. A. J. Luxemburg, A. C. Zaanen, Riesz space: Vol. I, North-Holland Publishing Co., Amsterdam-London (1971)
##[7]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
##[8]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica Sinica (English Series), 23 (2007), 2205-2212
##[9]
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]
Weak and strong convergence theorems for nonlinear mappings and system of generalized mixed equilibrium problems in Hilbert spaces
Weak and strong convergence theorems for nonlinear mappings and system of generalized mixed equilibrium problems in Hilbert spaces
en
en
In this paper, we construct two iteration schemes for approximating a common element of the set of solutions of equilibrium
problems (GMEP and GEP) and the set of common fixed points of a finite family of k-strictly asymptotically pseudo-contractions
in Hilbert spaces. Fixed point theorems are established in Hilbert spaces. Numerical examples and applications are provided.
The main results of this paper modify and improve many important recent results in the literature.
1433
1455
Qingqing
Cheng
Department of Mathematics and LPMC
Nankai University
China
chengqingqing2006@126.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
suyongfu@tjpu.edu.cn
Equilibrium problem
Modified Ishikawa’s iteration
hybrid algorithm
Hilbert space
weak and strong convergence.
Article.13.pdf
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[1]
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B. A. Bin Dehaish, X.-L. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
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S. Y. Cho, X.-L. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
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N.-N. Fang, Some results on split variational inclusion and fixed point problems in Hilbert spaces, Commun. Optim. Theory, 2017 (2017 ), 1-14
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X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488-502
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G. S. Saluja, Weak convergence theorems for nearly asymptotically nonexpansive mappings and asymptotically nonexpansive non-self mappings in uniformly convex Banach spaces, Commun. Optim. Theory, 2017 (2017 ), 1-23
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Y.-F. Su, M.-J. Shang, X.-L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal., 69 (2008), 2709-2719
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]
An extension of Furuta's log majorization inequality
An extension of Furuta's log majorization inequality
en
en
In this paper, we shall prove a log majorization inequality, which extends Furuta’s result.
1456
1458
Yanbo
Ren
School of Mathematics and Statistics
Henan University of Science and Technology
P. R. China
ryb7945@sina.com
Jian
Shi
College of Mathematics and Information Science
Hebei University
P. R. China
mathematic@126.com
Log majorization
Koizumi-Watanable inequality.
Article.14.pdf
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]
A note on spectral properties of a Dirac system with matrix coefficient
A note on spectral properties of a Dirac system with matrix coefficient
en
en
In this paper, we find a polynomial-type Jost solution of a self-adjoint matrix-valued discrete Dirac system. Then we
investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation theorem,
we prove that matrix-valued discrete Dirac system has continuous spectrum filling the segment [-2, 2]. Finally, we examine the
properties of the eigenvalues of this Dirac system and we prove that it has a finite number of simple real eigenvalues.
1459
1469
Yelda
Aygar
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
yaygar@ankara.edu.tr
Elgiz
Bairamov
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
bairamov.science.ankara.edu.tr
Seyhmus
Yardimci
Faculty of Science, Department of Mathematics
University of Ankara
Turkey
yardimci@ankara.edu.tr
Discrete Dirac system
spectral analysis
Jost solution
eigenvalue.
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]
Strong convergence theorems for a nonexpansive mapping and its applications for solving the split feasibility problem
Strong convergence theorems for a nonexpansive mapping and its applications for solving the split feasibility problem
en
en
The aim of this paper is to propose some novel algorithms and their strong convergence theorems for solving the split
feasibility problem, and we obtain the corresponding strong convergence results under mild conditions. The split feasibility
problem was proposed by [Y. Censor, Y. Elfving, Numer. Algorithms, 8 (1994), 221–239]. So far a lot of algorithms have been
given for solving this problem due to its applications in intensity-modulated radiation therapy, signal processing, and image
reconstruction. But most of these algorithms are of weak convergence. In this paper, we propose the new algorithms which can
provide useful guidelines for solving the relevant problem, such as the split common fixed point problem (SCFP), multi-set split
feasibility problem and so on.
1470
1477
Qinwei
Fan
School of Science
Xi’an Polytechnic University
P. R. China
qinweifan@126.com
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
P. R. China
yaozhsong@163.com
Split feasibility problem
strong convergence
nonexpansive mapping
Hilbert space.
Article.16.pdf
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[1]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
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C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
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L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
##[4]
Y. Censor, T. Borfeid, B. Martin, A. Troimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2005), 2353-2365
##[5]
Y. Censor, Y. Elfving, A multiprojection algorithm using Bregman projection in a product space, Numer. Algorithms, 8 (1994), 221-239
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Y. Censor, Y. Elfving, N. Kopf, T. Bottfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
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Q.-W. Fan, W. Wu, J. M. Zurada, Convergence of batch gradient learning with smoothing regularization and adaptive momentum for neural, SpringerPlus, 5 (2016), 1-17
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T.-H. Kim, H.-K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal., 61 (2005), 51-60
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R. Kraikaew, S. Saejung, On split common fixed point problems, J. Math. Anal. Appl., 415 (2014), 513-524
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A. Moudafi, A relaxed alternating CQ-algorithm for convex feasibility problems, Nonlinear Anal., 79 (2013), 117-121
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X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
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B. Qu, B.-H. Liu, N. Zheng, On the computation of the step-size for the CQ-like algorithms for the split feasibility problem, Appl. Math. Comput., 262 (2015), 218-223
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B. Qu, N.-H. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Problems, 21 (2005), 1655-1665
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B. Qu, N.-H. Xiu, A new halfspace-relaxation projection method for the split feasibility problem, Linear Algebra Appl., 428 (2008), 1218-1229
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W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
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Z.-W. Wang, Q.-Z. Yang, Y.-N. Yang, The relaxed inexact projection methods for the split feasibility problem, Appl. Math. Comput., 217 (2011), 5347-5359
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H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
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H.-K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 116 (2003), 659-678
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H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H.-K. Xu, A variable Krasonsel’skiî-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034
##[21]
H.-K. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems, 26 (2010), 1-17
##[22]
Q.-Z. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266
##[23]
Y.-H. Yao, R. P. Agarwal, M. Postolache, Y.-C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014 ), 1-14
##[24]
Y.-H. Yao, Y.-C. Liou, J.-C. Yao, Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory Appl., 2015 (2015), 1-19
##[25]
Y.-H. Yao, G. Marino, H.-K. Xu, Y.-C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 1-14
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Y.-H. Yao, M. Postolache, Y.-C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013), 1-12
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J.-L. Zhao, Q.-Z. Yang, Several solution methods for the split feasibility problem, Inverse Problems, 21 (2005), 1791-1799
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J.-L. Zhao, Y.-J. Zhang, Q.-Z. Yang, Modified projection methods for the split feasibility problem and the multiple-sets split feasibility problem, Appl. Math. Comput., 219 (2012), 1644-1653
]
An efficient computational technique for local fractional heat conduction equations in fractal media
An efficient computational technique for local fractional heat conduction equations in fractal media
en
en
The key aim of this article is to present an efficient numerical algorithm based on local fractional homotopy perturbation
Sumudu transform technique for solving local fractional heat-conduction equations in fractal media. The proposed technique
is an effective combination of local fractional homotopy perturbation method (LFHPM) and local fractional Sumudu transform
algorithm. The results obtained by using the suggested scheme show that the approach is straightforward to apply and very
accurate.
1478
1486
Duan
Zhao
IOT Perception Mine Research Center
The National and Local Joint Engineering Laboratory of Internet Application Technology on Mine
China University of Mining and Technology
China
China
Jagdev
Singh
Department of Mathematics
JECRC University
India
Devendra
Kumar
Department of Mathematics
JECRC University
India
Sushila
Rathore
Department of Physics
Vivekananda Global University
India
Xiao-Jun
Yang
School of Mechanics and Civil Engineering
State Key, Laboratory for Geomechanics and Deep Underground Engineering
China University of Mining and Technology
China University of Mining and Technology
China
China
dyangxiaojun@163.com
Heat conduction equation
fractal media
local fractional derivative
local fractional homotopy perturbation method
local fractional Sumudu transform method.
Article.17.pdf
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[1]
A. Atangana, Extension of the Sumudu homotopy perturbation method to an attractor for one-dimensional Keller-Segel equations, Appl. Math. Model., 39 (2015), 2909-2916
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A. Atangana, D. Baleanu, New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model , Therm. Sci., 20 (2016), 763-769
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D. Baleanu, H. M. Srivastava, X.-J. Yang, Local fractional variational iteration algorithms for the parabolic Fokker-Planck equation defined on Cantor sets, Prog. Fract. Differ. Appl., 1 (2015), 1-11
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J. Singh, D. Kumar, J. J. Nieto, A reliable algorithm for a local fractional Tricomi equation arising in fractal transonic flow, Entropy, 18 (2016), 1-8
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H. M. Srivastava, A. K. Golmankhaneh, D. Baleanu, X .J. Yang, Local fractional Sumudu transform with application to IVPs on Cantor sets, Abstr. Appl. Anal., 2014 (2014), 1-7
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]
Hermite pesudospectral method and modified Hermite spectral method for long-short wave equations
Hermite pesudospectral method and modified Hermite spectral method for long-short wave equations
en
en
We consider the initial boundary value problem of the long-short wave equations on the whole line. Firstly, a fully discrete
Hermite pseudospectral scheme and modified Hermite spectral scheme are structured basing Hermite functions, respectively.
Secondly, we analyze the two kinds of schemes theoretically. The modified Hermite spectral scheme shows the superiority in
priori estimates, numerical stability and convergence. Thirdly, numerical experiments for the two schemes are presented to
confirm our theoretical analysis.
1487
1511
Zeting
Liu
School of Mathematics and Systems Science & LMIB
Beihang University
China
lzt_well@163.com
Shujuan
Lü
School of Mathematics and Systems Science & LMIB
Beihang University
China
lsj@buaa.edu.cn
Long-short wave equations
Hermite pseudospectral method
modified Hermite spectral method
convergence
stability.
Article.18.pdf
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]
Null surfaces of null Cartan curves in Anti-de Sitter 3-space
Null surfaces of null Cartan curves in Anti-de Sitter 3-space
en
en
In this paper, we consider the null surfaces of null Cartan curves in Anti-de Sitter 3-space and making use of singularity
theory, we classify the singularities of the null surfaces and investigate the relationships between singularities of the null surfaces
and differential geometric invariants of null Cartan curves in Anti-de Sitter 3-space. Finally, we give an example to illustrate our
results.
1512
1523
Guangyu
Zhao
School of Mathematics and Statistics
Northeast Normal University
China
zhaogy291@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
China
peidh340@nenu.edu.cn
Yanlin
Li
School of Mathematics and Statistics
Northeast Normal University
China
liyl744@nenu.edu.cn
Zhigang
Wang
School of Mathematical Sciences
Harbin Normal University
China
wangzg2003205@163.com
Null Cartan curve
ruled null surface
principal normal indicatrix.
Article.19.pdf
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Common fixed points via implicit contractions on b-metric-like spaces
Common fixed points via implicit contractions on b-metric-like spaces
en
en
In this paper, we introduce some generalized nonlinear contractions via implicit functions and \(\alpha\)-admissible pair of mappings.
We also provide some common fixed point results for above contractions in the class of b-metric-like spaces. We will
derive some consequences and corollaries from our obtained results. Some illustrated examples are presented to make effective
the concepts and results.
1524
1537
Hassen
Aydi
Department of Mathematics, College of Education of Jubail
Department of Medical Research, China Medical University Hospital
Imam Abdulrahman Alfaisal University
China Medical University
Saudi Arabia
Taiwan
hmaydi@uod.edu.sa
Abdelbasset
Felhi
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
afelhi@kfu.edu.sa
Slah
Sahmim
Department of Mathematics and Statistics, College of Sciences
King Faisal University
Saudi Arabia
ssahmim@kfu.edu.sa
Common fixed point
implicit contraction
b-metric-like space.
Article.20.pdf
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M. U. Ali, T. Kamran, E. Karapınar, (\(\alpha,\psi,\xi\))-contractive multivalued mappings, Fixed Point Theory Appl., 2014 (2014 ), 1-8
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A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012 ), 1-10
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H. Aydi, \(\alpha\)-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations, Accepted in J. Nonlinear Convex Anal., (2015)
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H. Aydi, M. F. Bota, E. Karapınar, S. Moradi, A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337-346
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]
Stability of general virus dynamics models with both cellular and viral infections
Stability of general virus dynamics models with both cellular and viral infections
en
en
We consider two general models for the virus dynamics with virus-to-target and infected-to-target infections. We assume
that the virus-target and infected-target incidences, the production and clearance rates of all compartments are modeled by
general nonlinear functions which satisfy a set of reasonable conditions. We incorporate the latently infected cells in the second
model. For each model we prove the existence of the equilibria and calculate the basic reproduction number \(R_0\). We use suitable
Lyapunov functions and apply LaSalle’s invariance principle to prove the global asymptotic stability of the all equilibria of the
models. We confirm the theoretical results by numerical simulations.
1538
1560
A. M.
Elaiw
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
Al-Azhar University (Assiut Branch)
Saudi Arabia
Egypt
a_m_elaiw@yahoo.com
A. A.
Raezah
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science
King Abdulaziz University
King Khalid University
Saudi Arabia
Saudi Arabia
ahraizahah@gmail.com
A. M.
Shehata
Department of Mathematics, Faculty of Science
Al-Azhar University (Assiut Branch)
Egypt
Global stability
viral infection
cell-to-cell transfer
Lyapunov function.
Article.21.pdf
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[1]
N. Bairagi, D. Adak, Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay, Appl. Math. Model., 38 (2014), 5047-5066
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B. Buonomo, C. Vargas-De-León, Global stability for an HIV-1 infection model including an eclipse stage of infected cells, J. Math. Anal. Appl., 385 (2012), 709-720
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S.-S. Chen, C.-Y. Cheng, Y. Takeuchi, Stability analysis in delayed within-host viral dynamics with both viral and cellular infections, J. Math. Anal. Appl., 442 (2016), 642-672
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R. V. Culshaw, S.-G. Ruan, G. Webb, A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay, J. Math. Biol., 46 (2003), 425-444
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P. De Leenheer, H. L. Smith, Virus dynamics: a global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327
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A. M. Elaiw, Global properties of a class of HIV models, Nonlinear Anal. Real World Appl., 11 (2010), 2253-2263
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A. M. Elaiw, Global properties of a class of virus infection models with multitarget cells, Nonlinear Dynam., 69 (2012), 423-435
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A. M. Elaiw, N. A. Almuallem, Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells, Appl. Math. Comput., 265 (2015), 1067-1089
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A. M. Elaiw, N. A. Almuallem, Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells, Math. Methods Appl. Sci., 39 (2016), 4-31
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A. M. Elaiw, N. H. AlShamrani, Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal, Nonlinear Anal. Real World Appl., 26 (2015), 161-190
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A. M. Elaiw, N. H. AlShamrani, Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response, Math. Methods Appl. Sci., 40 (2017), 699-719
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A. M. Elaiw, S. A. Azoz, Global properties of a class of HIV infection models with Beddington-DeAngelis functional response, Math. Methods Appl. Sci., 36 (2013), 383-394
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A. M. Elaiw, I. Hassanien, S. Azoz, Global stability of HIV infection models with intracellular delays, J. Korean Math. Soc., 49 (2012), 779-794
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A. M. Elaiw, A. A. Raezah, A. S. Alofi, Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infectedto- target infections, AIP Adv., 6 (2016), 1-085204
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P. Georgescu, Y.-H. Hsieh, Global stability for a virus dynamics model with nonlinear incidence of infection and removal, SIAM J. Appl. Math., 67 (2006), 337-353
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K. Hattaf, N. Yousfi, A generalized virus dynamics model with cell-to-cell transmission and cure rate, Adv. Difference Equ., 2016 (2016), 1-11
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G. Huang, W.-B. Ma, Y. Takeuchi, Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 24 (2011), 1199-1203
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G. Huang, Y. Takeuchi, W.-B. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708
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D.-W. Huang, X. Zhang, Y.-F. Guo, H.-L.Wang, Analysis of an HIV infection model with treatments and delayed immune response, Appl. Math. Model., 40 (2016), 3081-3089
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X.-L. Lai, X.-F. Zou, Modeling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission, SIAM J. Appl. Math., 74 (2014), 898-917
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X.-L. Lai, X.-F. Zou, Modeling cell-to-cell spread of HIV-1 with logistic target cell growth, J. Math. Anal. Appl., 426 (2015), 563-584
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B. Li, Y.-M. Chen, X.-J. Lu, S.-Q. Liu, A delayed HIV-1 model with virus waning term, Math. Biosci. Eng., 13 (2016), 135-157
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M. Y. Li, L.-C.Wang, Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment, Nonlinear Anal. Real World Appl., 17 (2014), 147-160
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F. Li, J.-L. Wang, Analysis of an HIV infection model with logistic target-cell growth and cell-to-cell transmission, Chaos Solitons Fractals, 81 (2015), 136-145
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S.-Q. Liu, L. Wang, Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy, Math. Biosci. Eng., 7 (2010), 675-685
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M. C. Maheswari, P. Krishnapriya, K. Krishnan, M. Pitchai, A mathematical model of HIV-1 infection within host cell to cell viral transmissions with RTI and discrete delays, J. Appl. Math. Comput., (2018), 151-178
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C. C. McCluskey, Y. Yang, Global stability of a diffusive virus dynamics model with general incidence function and time delay, Nonlinear Anal. Real World Appl., 25 (2015), 64-78
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C. Monica, M. Pitchaimani, Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays, Nonlinear Anal. Real World Appl., 27 (2016), 55-69
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A. U. Neumann, N. P. Lam, H. Dahari, D. R. Gretch, T. E. Wiley, T. J. Layden, A. S. Perelson, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-\(\alpha\) therapy, Science, 282 (1998), 103-107
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P. K. Roy, A. N. Chatterjee, D. Greenhalgh, Q. J. A. Khan, Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model, Nonlinear Anal. Real World Appl., 14 (2013), 1621-1633
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X.-G. Shi, X.-Y. Zhou, X.-Y. Son, Dynamical behavior of a delay virus dynamics model with CTL immune response, Nonlinear Anal. Real World Appl., 11 (2010), 1795-1809
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H.-Y. Shu, L. Wang, J. Watmough, Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses, SIAM J. Appl. Math., 73 (2013), 1280-1302
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X.-Y. Song, A. U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl., 329 (2007), 281-297
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K. Wang, A.-J. Fan, A. Torres, Global properties of an improved hepatitis B virus model, Nonlinear Anal. Real World Appl., 11 (2010), 3131-3138
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J.-L. Wang, M. Guo, X.-N. Liu, Z.-T. Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Appl. Math. Comput., 291 (2016), 149-161
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L.-C. Wang, M. Y. Li, D. Kirschner, Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci., 179 (2002), 207-217
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J.-L. Wang, J. Yang, T. Kuniya, Dynamics of a PDE viral infection model incorporating cell-to-cell transmission, J. Math. Anal. Appl., 444 (2016), 1542-1564
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S.-H. Xu, Global stability of the virus dynamics model with Crowley-Martin functional response, Electron. J. Qual. Theory Differ. Equ., 2012 (2012 ), 1-10
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Y. Yang, J.-L. Zhou, X.-S. Ma, T.-H. Zhang, Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions, Comput. Math. Appl., 72 (2016), 1013-1020
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Y. Yang, L. Zou, S.-G. Ruan, Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Math. Biosci., 270 (2015), 183-191
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Y.-Q. Zhao, D. T. Dimitrov, H. Liu, Y. Kuang, Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions, Bull. Math. Biol., 75 (2013), 649-675
]
Approximation on the rotation group SO(3)
Approximation on the rotation group SO(3)
en
en
In this paper we study the approximation on rotation group SO(3), we consider the partial sum, Fejér and Jackson-type
operators and obtain the approximation theorems in \(L_p(1 \leq p \leq\infty)\) respectively
1561
1568
Zhuyuan
Yang
School of Mathematics and Computer Science
Yunnan Minzu University
P. R. China
yangzhuyuan@sina.com
Xin
Wang
School of Mathematics and Computer Science
Yunnan Minzu University
P. R. China
wxkmyn@163.com
Xinzhi
Liu
Department of Mathematics
University of Waterloo
Canada N2L 3G1
xinzhi.liu@uwarterloo.ca
Rotation group
operator
approximation.
Article.22.pdf
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D. I. Cartwright, K. Kucharski, Jackson’s theorem for compact connected Lie groups, J. Approx. Theory, 55 (1988), 352-359
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S. Gong, Dianxing qun shangde tiaohe fenxi, (Chinese) [[Harmonic analysis on classical groups]] Chuncui Shuxue yu Yingyong Shuxue Zhuanzhu [Series of Monographs in Pure and Applied Mathematics], Kexue Chubanshe (Science Press), Beijing (1983)
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Q.-Z. Han, H.-Z. Sun, Group theory, Peking University Press, Beijing (1987)
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R. Hielscher, J. Prestin, A. Vollrath, Fast summation of functions on the rotation group, Math. Geosci., 42 (2010), 773-794
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]
On some fixed points of \(\alpha-\psi\) contractive mappings with rational expressions
On some fixed points of \(\alpha-\psi\) contractive mappings with rational expressions
en
en
In this paper, we study the existence and uniqueness of fixed points for a new class of contractive mappings involving
rational expressions, which enable us to extend many known results in the literature. We consider illustrative example and
consequences to underline the novelty of the main results.
1569
1581
Erdal
Karapinar
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
King Abdulaziz University
S. A
erdalkarapinar@yahoo.com
Abdelkader
Dehici
Department of Mathematics and Informatics
University of Souk-Ahras
Algeria
dehicikader@yahoo.fr
Nadjeh
Redjel
Department of Mathematics
University of Constantine 1
Algeria
najehredjel@yahoo.fr
Complete metric space
(c)-comparison function
fixed point
\(\alpha\)-admissible mapping
cyclic mapping.
Article.23.pdf
[
[1]
R. P. Agarwal, M. A. Alghamdi, N. Shahzad, Fixed point theory for cyclic generalized contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-11
##[2]
M. U. Ali, T. Kamran, E. Karapınar, A new approach to (\(\alpha,\psi\))-contractive nonself multivalued mappings, J. Inequal. Appl., 2014 (2014), 1-9
##[3]
M. U. Ali, T. Kamran, E. Karapınar, Fixed point of \(\alpha-\psi\)-contractive type mappings in uniform spaces, Fixed Point Theory Appl., 2014 (2014 ), 1-12
##[4]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[5]
V. Berinde, Contracţii generalizate şi aplicaţii, (Romanian) [[Generalized contractions and applications]] Colecia Universitaria (Baia Mare) [University Collection], Editura Cub Press, Baia Mare (1997)
##[6]
V. Berinde, Iterative approximation of fixed points, Editura Efemeride, Baia Mare (2002)
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\) -contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
]
The modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces
The modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces
en
en
The aim of this paper is to establish the modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive
mappings in Banach spaces. The strong convergence theorems of the rules are proved under certain assumptions
imposed on the sequences of parameters. As an application, we apply our main results to solve some variational inequalities
in Banach spaces, provided T is asymptotically regular. Our results extend the previous known results from Hilbert spaces to
Banach spaces and from non-expansive mappings to asymptotically pseudocontractive mappings.
1582
1592
Yuanheng
Wang
Department of Mathematics
Zhejiang Normal University
China
yhwang@zjnu.cn
Chanjuan
Pan
Department of Mathematics
Zhejiang Normal University
China
cjpanzjnu@163.com
Viscosity implicit rule
variational inequality
strong convergence
asymptotically pseudo-contractions
Banach space.
Article.24.pdf
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[1]
G. Cai, S.-Q. Bu, Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems, Comput. Math. Appl., 62 (2011), 4772-4782
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L.-C. Ceng, S. Al-Homidan, Q. H. Ansari, J.-C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math., 223 (2009), 967-974
##[3]
F. Gu, A new hybrid iteration method for a finite family of asymptotically nonexpansive mappings in Banach spaces, Fixed Point Theory Appl., 2013 (2013 ), 1-10
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A. Kangtunyakarn, S. Suantai, A new mapping for finding common solutions of equilibrium problems and fixed point problems of finite family of nonexpansive mappings, Nonlinear Anal., 71 (2009), 4448-4460
##[5]
Y.-F. Ke, C.-F. Ma, A new relaxed extragradient-like algorithm for approaching common solutions of generalized mixed equilibrium problems, a more general system of variational inequalities and a fixed point problem, Fixed Point Theory Appl., 2013 (2013 ), 1-21
##[6]
J. Lou, L.-J. Zhang, Z. He, Viscosity approximation methods for asymptotically nonexpansive mappings, Appl. Math. Comput., 203 (2008), 171-177
##[7]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
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X.-L. Qin, Y. J. Cho, S. M. Kang, Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal., 72 (2010), 99-112
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Y.-H. Wang, Y.-H. Xia, Strong convergence for asymptotically pseudocontractions with the demiclosedness principle in Banach spaces, Fixed Point Theory Appl., 2012 (2012 ), 1-8
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Y. H. Wang, L. C. Zeng, Convergence of generalized projective modified iteration methods in Banach spaces, (Chinese) Chinese Ann. Math. Ser. A, 30 (2009), 55-62
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H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015 ), 1-12
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Y.-H. Yao, Y.-C. Liou, R.-D. Chen, Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces, Nonlinear Anal., 67 (2007), 3311-3317
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Y.-H. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015 ), 1-15
##[15]
Y.-L. Yu, C.-F. Wen, A modified iterative algorithm for nonexpansive mappings, J. Nonlinear Sci. Appl., 9 (2016), 3719-3726
]
Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay
Finite-gain \(L_\infty\) stability from disturbance to output of impulsive systems with time delay
en
en
This paper studies finite-gain \(L_\infty\) stability from disturbance to output of delayed impulsive systems. By employing the
method of Lyapunov function, several criteria of finite-gain \(L_\infty\) stability from disturbance to output are established. It shows
that the linear delayed differential systems can be finite-gain \(L_\infty\)stabilized from disturbance to output using impulsive feedback
control even there is unstable matrix. Moreover, delayed differential equations also may be finite-gain \(L_\infty\) stable from disturbance
to output under an appropriate sequence of impulses treated as disturbances. Two examples and their simulations are also given
to illustrate our results.
1593
1602
Ping
Li
School of Computer Science and Technology
Department of Applied Mathematics
Southwest Minzu University
University of Waterloo
P. R. China
Canada N2L 3G1
liping925@126.com
Xinzhi
Liu
Department of Applied Mathematics
University of Waterloo
Canada N2L 3G1
xinzhi.liu@uwaterloo.ca
Wu
Zhao
School of Management and Economics
University of Electronic Science and Technology of China
P. R. China
zhaowu@uestc.edu.cn
Impulsive control
impulsive disturbance
Lyapunov function
finite-gain \(L_\infty\) stability.
Article.25.pdf
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[1]
K. Akbari Moornani, M. Haeri, Necessary and sufficient conditions for BIBO-stability of some fractional delay systems of neutral type, IEEE Trans. Automat. Control, 56 (2011), 125-128
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F. Amato, G. De Tommasi, A. Pironti, Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems, Automatica J. IFAC, 49 (2013), 2546-2550
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C. Bonnet, J. R. Partington, Analysis of fractional delay systems of retarded and neutral type, Automatica J. IFAC, 38 (2002), 1133-1138
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J. Carvajal, G.-R. Chen, H. Ogmen, Fuzzy PID controller: design, performance evaluation, and stability analysis, Analytical theory of fuzzy control with applications, Inform. Sci., 123 (2000), 249-270
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Y. Ji, X.-M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks, Circuits Systems Signal Process., 34 (2015), 1499-1517
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H. K. Khalil, Nonlinear systems, Third edition, Prentice-Hall, Upper Saddle River, NJ (2002)
##[7]
P. Li, S.-M. Zhong, BIBO stabilization of time-delayed system with nonlinear perturbation, Appl. Math. Comput., 195 (2008), 264-269
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P. Li, S.-M. Zhong, J.-Z.Cui , Delay-dependent robust BIBO stabilization of uncertain system via LMI approach, Chaos Solitons Fractals, 40 (2009), 1021-1028
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J.-Q. Lu, D. W. C. Ho, J.-D. Cao, A unified synchronization criterion for impulsive dynamical networks, Automatica J. IFAC, 46 (2010), 1215-1221
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A. Möller, U. T. Jönsson, Input-output analysis of power control in wireless networks, IEEE Trans. Automat. Control, 58 (2013), 834-846
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P. Naghshtabrizi, J. P. Hespanha, A. R. Teel, Stability of delay impulsive systems with application to networked control systems, Trans. Inst. Measurement Control, 32 (2010), 511-528
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J. R. Partington, C. Bonnet, \(H_\infty\) and BIBO stabilization of delay systems of neutral type, Syst. Control Lett., 52 (2004), 283-288
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K.-B. Shi, Y.-Y. Tang, X.-Z. Liu, S.-M. Zhong, Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation, ISA Trans., 66 (2017), 185-199
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A. R. Teel, T. T. Georgiou, L. Praly, E. D. Sontag, Input-output stability, W.S. Levine (Ed.), The Control Handbook, CRC Press, Boca Raton, FL, (1996), 895-908
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W.-A. Zhang, L. Yu, A robust control approach to stabilization of networked control systems with time-varying delays, Automatica J. IFAC, 45 (2009), 2440-2445
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L. Zhao, H.-J. Gao, H. R. Karimi, Robust stability and stabilization of uncertain T-S fuzzy systems with time-varying delay: an input-output approach, IEEE Trans. Fuzzy Syst., 21 (2013), 883-897
]
Fujita type theorems for a class of semilinear parabolic equations with a gradient term
Fujita type theorems for a class of semilinear parabolic equations with a gradient term
en
en
This paper concerns the asymptotic behavior of solutions to the Neumann exterior problem of a class of semilinear parabolic
equations with a gradient term. The blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated
by spacial dimension, the behavior of the coefficient of the gradient term at infinity and other exponents.
1603
1612
Yuanyuan
Nie
School of Mathematics
Jilin University
China
Mingjun
Zhou
School of Mathematics
Jilin University
China
Qian
Zhou
School of Mathematics
Jilin University
China
zhouqian@jlu.edu.cn
Yang
Na
School of Mathematics
Jilin University
China
Critical Fujita exponent
gradient term.
Article.26.pdf
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D. Andreucci, G. R. Cirmi, S. Leonardi, A. F. Tedeev, Large time behavior of solutions to the Neumann problem for a quasilinear second order degenerate parabolic equation in domains with noncompact boundary, J. Differential Equations, 174 (2001), 253-288
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K. Deng, H. A. Levine, The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl., 243 (2000), 85-126
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M. Fira, B. Kawohl, Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition, Adv. Math. Sci. Appl., 11 (2001), 113-126
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C.-P. Wang, S.-N. Zheng, Critical Fujita exponents of degenerate and singular parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 136 (2006), 415-430
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C.-P. Wang, S.-N. Zheng, Fujita-type theorems for a class of nonlinear diffusion equations, Differential Integral Equations, 26 (2013), 555-570
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M. Winkler, A critical exponent in a degenerate parabolic equation, Math. Methods Appl. Sci., 25 (2002), 911-925
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Q. S. Zhang, A general blow-up result on nonlinear boundary-value problems on exterior domains, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 451-475
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S.-N. Zheng, C.-P. Wang, Large time behaviour of solutions to a class of quasilinear parabolic equations with convection terms, Nonlinearity, 21 (2008), 2179-2200
##[20]
Q. Zhou, Y.-Y. Nie, X.-Y. Han, Large time behavior of solutions to semilinear parabolic equations with gradient, J. Dyn. Control Syst., 22 (2016), 191-205
]
\(S-\gamma-\phi-\varphi\)-contractive type mappings in \(S\)-metric spaces
\(S-\gamma-\phi-\varphi\)-contractive type mappings in \(S\)-metric spaces
en
en
In this paper, we introduce several types of \(S-\gamma-\phi-\varphi\)-contractive mappings which are generalizations of \(\alpha-\psi\) -contractive
mappings [B. Samet, C. Vetro, P. Vetro, Nonlinear Anal., 75 (2012), 2154–2165] in the structure of S-metric spaces. Furthermore, we
prove existence and uniqueness of fixed points and common fixed points of such contractive mappings. Our results generalize,
extend and improve the existing results in the literature. We also state some illustrative examples to support our results.
1613
1639
Mi
Zhou
School of Science and Technology
Sanya College
China
mizhou330@126.com
Xiao-lan
Liu
College of Science
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing
Sichuan University of Science and Engineering
China
China
stellalwp@163.com
Stojan
Radenovic
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.rs
S-metric space
\(S-\gamma-\phi-\varphi\)-contractive mappings
fixed point.
Article.27.pdf
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[1]
R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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V. Berinde, Iterative approximation of fixed points, Second edition. Lecture Notes in Mathematics, Springer, Berlin (2007)
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A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536
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M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly, 116 (2009), 708-718
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N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-17
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S. Gähler, Über die Uniformisierbarkeit 2-metrischer Räume, (German) Math. Nachr., 28 (1964/1965), 235-244
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T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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R. Kannan, Some results on fixed points, II, Amer. Math. Monthly, 76 (1969), 405-408
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E. Karapınar, B. Samet, Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012 ), 1-17
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V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
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Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
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J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212
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S. Radenović, Bhaskar-Lakshmikantham type results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 96-103
##[18]
S. Radenović, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math., 38 (2014), 249-257
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S. Radenović, Some coupled coincidence points results of monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 174-184
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
##[21]
R. Saadati, S. M. Vaezpour, Monotone generalized weak contractions in partially ordered metric spaces, Fixed Point Theory, 11 (2010), 375-382
##[22]
B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 2010 (2010), 4508-4517
##[23]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[24]
S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik, 66 (2014), 113-124
##[25]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266
##[26]
S. Sedghi, N. Shobe, H.-Y. Zhou, A common fixed point theorem in \(D^*\)-metric spaces, Fixed Point Theory Appl., 2007 (2007), 1-13
##[27]
M. Turinici, Abstract comparison principles and multivariable Gronwall-Bellman inequalities, J. Math. Anal. Appl., 117 (1986), 100-127
##[28]
M. Zhou, X.-L. Liu, On coupled common fixed point theorems for nonlinear contractions with the mixed weakly monotone property in partially ordered S-metric spaces, J. Funct. Spaces, 2016 (2016 ), 1-9
]
F-sensitivity and (\(F_1, F_2\))-sensitivity between dynamical systems and their induced hyperspace dynamical systems
F-sensitivity and (\(F_1, F_2\))-sensitivity between dynamical systems and their induced hyperspace dynamical systems
en
en
The notions of \(F\)-sensitivity and (\(F_1, F_2\))-sensitivity were introduced and studied by Wang et al. via Furstenberg families
in [H.-Y. Wang, J.-C. Xiong, F. Tan, Discrete Dyn. Nat. Soc., 2010 (2010), 12 pages]. In this paper, the concepts of \(F\)-collective
sensitivity (resp. (\(F_1, F_2\))-collective sensitivity) and compact-type \(F\)-collective sensitivity (resp. compact-type (\(F_1, F_2\))-collective
sensitivity) are introduced as stronger forms of the traditional sensitivity for dynamical systems and Hausdorff locally compact
second countable (HLCSC) dynamical systems, respectively, where \(F,F_1\) and \(F_2\) are Furstenberg families. It is proved that
\(F\)-sensitivity (resp. (\(F_1, F_2\))-sensitivity) of the induced hyperspace system defined on the space of non-empty compact subsets
or non-empty finite subsets (Vietoris topology) is equivalent to the \(F\)-collective sensitivity (resp. (\(F_1, F_2\))-collective sensitivity) of
the original system; F-sensitivity (resp. (\(F_1, F_2\))-sensitivity) of the induced hyperspace system defined on the space of all nonempty
closed subsets (hit-or-miss topology) is equivalent to the compact-type \(F\)-collective sensitivity (resp. (\(F_1, F_2\))-collective
sensitivity) of the original HLCSC system. Moreover, it is shown that for a given dynamical system (E, d, f) and a given
Furstenberg family F, if (E, d, f) is F-mixing, then it is \(F\)-collectively sensitive. Additionally, we prove that for a given dynamical
system (E, d, f) and a given Furstenberg family \(F, (E, d, f)\) is \(F\)-mixing if and only if \(\underbrace{f\times f\times...\times f}_n\)
is \(F\)-mixing for every \(n\geq 2\).
Our results extend and improve some existing results.
1640
1651
Risong
Li
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Yu
Zhao
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
datom@189.cn
Hongqing
Wang
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
wanghq3333@126.com
Ru
Jiang
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
jiru1995@163.com
Haihua
Liang
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
lhhlucy@126.com
Furstenberg families
\(F\)-collective sensitivity
compact-type \(F\)-collective sensitivity
hyperspace dynamical systems
compact-type (\(F_1، F_2\))-collective sensitivity
(\(F_1،F_2\))-collective sensitivity
hit-or-miss topology.
Article.28.pdf
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J. Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals, 25 (2005), 681-685
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G. Beer, Topologies on closed and closed convex sets, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1993)
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D. Kwietniak, P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals, 33 (2007), 76-86
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R.-S. Li, Y.-M. Shi, Stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces, Abstr. Appl. Anal., 2014 (2014 ), 1-10
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G.-F. Liao, X.-F. Ma, L.-D. Wang, Individual chaos implies collective chaos for weakly mixing discrete dynamical systems, Chaos Solitons Fractals, 32 (2007), 604-608
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G.-F. Liao, L.-D. Wang, Y.-C. Zhang, Transitivity, mixing and chaos for a class of set-valued mappings, Sci. China Ser. A, 49 (2006), 1-8
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X.-F. Ma, B.-Z. Hou, G.-F. Liao, Chaos in hyperspace system, Chaos Solitons Fractals, 40 (2009), 653-660
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]
Comparable nonlinear contractions in ordered metric spaces
Comparable nonlinear contractions in ordered metric spaces
en
en
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-
continuity and compatibility to order-theoretic setting especially in ordered metric spaces and utilize these relatively weaker
notions to prove some existence and uniqueness results on coincidence points for g-comparable mappings satisfying Boyd-Wong
type nonlinear contractivity conditions. We also furnish some illustrative examples to demonstrate our results. Finally, as an
application of our certain newly proved results, we establish the existence and uniqueness of solution of an integral equation.
1652
1674
Aftab
Alam
Department of Mathematics
Aligarh Muslim University
India
aafu.amu@gmail.com
Qamrul Haq
Khan
Department of Mathematics
Aligarh Muslim University
India
qhkhan.ssitm@gmail.com
Mohammad
Imdad
Department of Mathematics
Aligarh Muslim University
India
mhimdad@yahoo.co.in
Ordered metric space
TCC property
g-comparable mappings
g-admissible mappings
termwise monotone sequence.
Article.29.pdf
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]
Chaos in a topologically transitive semi-flow
Chaos in a topologically transitive semi-flow
en
en
In this paper, we study the chaotic phenomena in a topologically transitive, continuous semi-flow, and show that the
erratic time dependence of orbits in such a semi-flow is more complicated than the one described by Li-Yorke chaos. Also,
we generalize the notion of sensitive dependence on initial conditions for semi-flows and explore the chaotic phenomena for
topologically transitive, continuous semi-flows with the generalized sensitivity property. Our results extend the existing results
to semi-flows.
1675
1682
Risong
Li
School of Mathematic and Computer Science
Guangdong Ocean University
P. R. China
gdoulrs@163.com
Tianxiu
Lu
Department of Mathematics
Sichuan University of Science and Engineering
P. R. China
lubeeltx@163.com
Chaos
topological transitivity
sensitive dependence.
Article.30.pdf
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]
Fourier series of sums of products of Genocchi functions and their applications
Fourier series of sums of products of Genocchi functions and their applications
en
en
Recently, Luo introduced Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Genocchi polynomials and investigated
some interesting identities and properties of these polynomials by using Fourier series. In this paper, we consider three
types of functions given by sums of products of Genocchi functions and derive their Fourier series expansions. In addition, we
will express each of them in terms of Bernoulli functions.
1683
1694
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Gwan-Woo
Jang
Department of Mathematics
Kwangwoon University
Republic of Korea
jgw5687@naver.com
Jongkyum
Kwon
Department of Mathematics Education and RINS
Gyeongsang National University
Republic of Korea
mathkjk26@gnu.ac.kr
Fourier series
Genocchi functions
Genocchi polynomials.
Article.31.pdf
[
[1]
A. Bayad, T. Kim, Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 247-253
##[2]
A. Bayad, T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18 (2011), 133-143
##[3]
A. Bayad, T. Kim, Higher recurrences for Apostol-Bernoulli-Euler numbers, Russ. J. Math. Phys., 19 (2012), 1-10
##[4]
G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225-249
##[5]
C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173-199
##[6]
T. Kim, A note on the q-Genocchi numbers and polynomials, J. Inequal. Appl., 2007 (2007), 1-8
##[7]
T. Kim, On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl., 326 (2007), 1458-1465
##[8]
T. Kim, Euler numbers and polynomials associated with zeta functions, Abstr. Appl. Anal., 2008 (2008), 1-11
##[9]
T. Kim, Note on the Euler numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 17 (2008), 131-136
##[10]
T. Kim, On the multiple q-Genocchi and Euler numbers, Russ. J. Math. Phys., 15 (2008), 481-486
##[11]
T. Kim, Some identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 20 (2010), 23-28
##[12]
D. S. Kim, T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci., 2012 (2012), 1-12
##[13]
D. S. Kim, T. Kim, Euler basis, identities, and their applications, Int. J. Math. Math. Sci., 2012 (2012), 1-15
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D. S. Kim, T. Kim, A note on higher-order Bernoulli polynomials, J. Inequal. Appl., 2013 (2013), 1-9
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D. S. Kim, T. Kim, Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct., 24 (2013), 734-738
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D. S. Kim, T. Kim, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196-208
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T. Kim, D. S. Kim, S.-H. Rim, D. V. Dolgy, Fourier series of higher-order Bernoulli functions and their applications, J. Inequal. Appl., 2017 (2017), 1-7
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Q.-M. Luo, Extensions of the Genocchi polynomials and their Fourier expansions and integral representations, Osaka J. Math., 48 (2011), 291-309
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]
Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space
Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space
en
en
In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of
order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space
and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main
results and to show the essentiality of the given hypotheses.
1695
1708
M. M. M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
mmjst4@qu.edu.qa
Z.
Mustafa
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
zead@qu.edu.qa
A. H.
Ansari
Department of Mathematics
Karaj Branch, Islamic Azad University
Iran
mathanalsisamir4@gmail.com
S.
Chandok
School Of Mathematics
Thapar University
India
chansok.s@gmail.com;sumit.chandok@thapar.edu
C.
Dolićanin
Department of Matheamtics
State University of Novi Pazar
Serbia
cdolicanin@np.ac.rs
\(\varepsilon\)-fixed point
\(\alpha\)-admissible
partial (h-F)-generalized convex contractions of order 3
partial (h-F)-subgeneralized convex contractions of order 3
\(\alpha\)-complete metric spaces
graph.
Article.32.pdf
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A. H. Ansari, Note on \(\alpha\)-admissible mappings and related fixed point theorems, The 2nd Regional Conference on mathematics and Applications, PNU, Iran, September , (2014), 373-376
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A. H. Ansari, S. Chandok, C. Ionescu, Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 2014 (2014 ), 1-17
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N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014 ), 1-11
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S. Tijs, A. Torre, R. Branzei, Approximate fixed point theorems, Miron Nicolescu (1903–1975) and Nicolae Ciorănescu (1903–1957), Libertas Math., 23 (2003), 35-39
]
On some new variations of Hardy type inequalities
On some new variations of Hardy type inequalities
en
en
The goal of this paper is to establish some new variations of the inequalities which originate from the well-known Hardy
type inequalities. The method applied in this paper to achieve our results is related to the idea used by Levinson to obtain the
generalizations of Hardy’s integral inequality.
1709
1713
Zareen A.
Khan
Department of Mathematics
Princess Nora Bint Abdul Rahman University
KSA
faascsm@ku.ac.th
Hardy type inequality
Hölder’s inequality.
Article.33.pdf
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G. H. Hardy, Note on a theorem of Hilbert, Math. Z., 6 (1920), 314-317
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G. H. Hardy, J. E. Littlewood, G. Pólya , Inequalities, 2d ed., Cambridge, at the University Press (1952)
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Some fractional extensions of trapezium inequalities via coordinated harmonic convex functions
Some fractional extensions of trapezium inequalities via coordinated harmonic convex functions
en
en
In this article, we derive a new fractional estimate for Hermite-Hadamard’s inequality via coordinated harmonic convex
functions on a rectangle from the plane \(\mathbb{R}^2\). We establish a new fractional integral identity for partially differentiable functions.
Utilizing this integral identity, we obtain some more fractional estimates for Hermite-Hadamard’s inequality. The ideas of this
paper may stimulate further research.
1714
1730
Muhammad Uzair
Awan
Government College University
Pakistan
awan.uzair@gmail.com
Muhammad Aslam
Noor
Mathematics Department
Mathematics Department
King Saud University
COMSATS Institute of Information, Technology
Saudi Arabia
Pakistan
noormaslam@gmail.com
Marcela V.
Mihai
Department scientific-methodical sessions
Romanian Mathematical Society-branch Bucharest
Romania
marcelamihai58@yahoo.com
Khalida Inayat
Noor
COMSATS Institute of Information Technology
Pakistan
khalidanoor@hotmail.com
Harmonic convex functions
fractional
trapezium
Hermite-Hadamard inequalities.
Article.34.pdf
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[1]
G. Cristescu, L. Lupşa, Non-connected convexities and applications, Applied Optimization, Kluwer Academic Publishers, Dordrecht (2002)
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G. Cristescu, M. A. Noor, M. U. Awan, Bounds of the second degree cumulative frontier gaps of functions with generalized convexity, Carpathian J. Math., 31 (2015), 173-180
##[3]
S. S. Dragomir, On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775-788
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I. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (2014), 935-942
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I. İşcan, S.-H. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014), 237-244
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M. A. Noor, K. I. Noor, M. U. Awan, Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17 (2014), 51-61
##[14]
M. A. Noor, K. I. Noor, M. U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equ., 60 (2015), 776-786
##[15]
M. A. Noor, K. I. Noor, M. U. Awan, S. Costache, Some integral inequalities for harmonically h-convex functions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 77 (2015), 5-16
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M. E. Ozdemir, C . Yıldız, A. O. Akdemir, On the co-ordinated convex functions, Appl. Math. Inf. Sci., 8 (2014), 1085-1091
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J. Park, Hermite-Hadamard-like and Simpson-like type inequalities for harmonically convex functions, Int. J. Math. Anal., 8 (2014), 1321-1337
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M. Z. Sarıkaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms Spec. Funct., 25 (2014), 134-147
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]
Some Coupled fixed point theorems in partially ordered \(A_b\)-metric space
Some Coupled fixed point theorems in partially ordered \(A_b\)-metric space
en
en
In this paper, we use the concept of \(A_b\)-metric space which is obtained by generalizing the definitions of \(A\)-metric space and
b-metrc space. Using this concept, we prove some coupled fixed point theorems in partially ordered \(A_b\)-metric space. Examples
are also presented to verify the obtained results.
1731
1743
N.
Mlaiki
Department of Mathematical Sciences
Prince Sultan University
Saudi Arabia
nmlaiki@psu.edu.sa
Y.
Rohen
Department of Mathematics
NIT Manipur
India
ymnehor2008@yahoo.com
Common fixed points
\(A\)-metric space
b-metric space
\(A_b\)-metric space.
Article.35.pdf
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[1]
M. Abbas, B. Ali, Y. I Suleiman, Generalized coupled common fixed point results in partially ordered A-metric spaces, Fixed point theory Appl., 2015 (2015 ), 1-24
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A. Aghajani, M. Abbas, E. Pourhadi Kallehbasti, Coupled fixed point theorems in partially ordered metric spaces and application, Math. Commun., 17 (2012), 497-509
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M. Ughade, D. Turkoglu, S. R. Singh, R. D. Daheriya, Some fixed point theorems in \(A_b\)-metric space, British J. Math. Comput. Sci., 19 (2016), 1-24
]
On double Natural transform and its applications
On double Natural transform and its applications
en
en
In this work, we generalize the concept of one dimensional Natural transform to two dimensional Natural transform namely,
double Natural transform and some of its properties are given. We also set a relation between double Natural transform and
double Laplace, double Sumudu transforms. Further the convolution theorem with a proof is investigated with some details.
Double Natural transform is applied to get the solutions of some general linear telegraphs, wave and partial integro-differential
equations.
1744
1754
Adem
Kılıçman
Department of Mathematics and Institute for Mathematical Research
University Putra Malaysia
Malaysia
akilic@upm.edu.my
Maryam
Omran
Institute for Mathematical Research
University Putra Malaysia
Malaysia
maryamomran83@yahoo.com
Double Natural transform
single Natural transform
partial differential and integro-differential equations
convolution theorem.
Article.36.pdf
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[1]
S. K. Q. Al-Omari, On the application of natural transforms, Inter. J. Pure Appl. Math., 85 (2013), 729-744
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M. Omran, A. Kılıçman, Natural transform of fractional order and some properties, Cogent Math., 3 (2016), 1-8
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]
Some new bounds for Simpson's rule involving special functions via harmonic h-convexity
Some new bounds for Simpson's rule involving special functions via harmonic h-convexity
en
en
In this article, we obtain some new bounds for Simpson’s rule via harmonic h-convex functions. We also point out some
new and known special cases which can be deduced from main results of the article. Some applications to special means are
also discussed.
1755
1766
Muhammad Uzair
Awan
Government College University
Pakistan
awan.uzair@gmail.com
Muhammad Aslam
Noor
Department of Mathematics
Mathematics Department
King Saud University
COMSATS Institute of Information Technology
Saudi Arabia
Pakistan
noormaslam@gmail.com
Marcela V.
Mihai
Department scientific-methodical sessions
Romanian Mathematical Society-branch Bucharest
Romania
marcelamihai58@yahoo.com
Khalida Inayat
Noor
COMSATS Institute of Information Technology
Pakistan
khalidanoor@hotmail.com
Awais Gul
Khan
Government College University
Pakistan
awaisgulkhan@gmail.com
Convex functions
bounds
harmonic
differentiable
Simpson inequality.
Article.37.pdf
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[1]
M. Alomari, M. Darus, On some inequalities of Simpson-type via quasi-convex functions and applications, Transylv. J. Math. Mech., 2 (2010), 15-24
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W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, (German) Publ. Inst. Math. (Beograd) (N.S.), 23(37) (1978), 13-20
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G. Cristescu, L. Lupşa, Non-connected convexities and applications, Applied Optimization, Kluwer Academic Publishers, Dordrecht (2002)
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G. Cristescu, M. A. Noor, M. U. Awan, Bounds of the second degree cumulative frontier gaps of functions with generalized convexity, Carpathian J. Math., 31 (2015), 173-180
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S. S. Dragomir , Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, RGMIA Res. Rep. Coll., Article 72 (2013)
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S. S. Dragomir, R. P. Agarwal, P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl., 5 (2000), 533-579
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I. İşcan, Hermite-Hadamard and Simpson-like type inequalities for differentiable harmonically convex functions, J. Math., 2014 (2014 ), 1-10
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I. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (2014), 935-942
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I. İşcan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp J. Math., 3 (2015), 63-74
##[13]
M. V. Mihai, M. A. Noor, K. I. Noor, M. U. Awan, Some integral inequalities for harmonic h-convex functions involving hypergeometric functions, Appl. Math. Comput., 252 (2015), 257-262
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M. A. Noor, G. Cristescu, M. U. Awan, Generalized fractional Hermite-Hadamard inequalities for twice differentiable s-convex functions, Filomat, 29 (2015), 807-815
##[15]
M. A. Noor, K. I. Noor, M. U. Awan, Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17 (2014), 51-61
##[16]
M. A. Noor, K. I. Noor, M. U. Awan, Integral inequalities for coordinated harmonically convex functions, Complex Var. Elliptic Equ., 60 (2015), 776-786
##[17]
M. A. Noor, K. I. Noor, M. U. Awan, S. Costache, Some integral inequalities for harmonically h-convex functions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 77 (2015), 5-16
##[18]
J. Park, Hermite-Hadamard-like and Simpson-like type inequalities for harmonically convex functions, Int. J. Math. Anal., 8 (2014), 1321-1337
##[19]
M. Z. Sarikaya, E. Set, M. E. Ozdemir, On new inequalities of Simpson’s type for s-convex functions, Comput. Math. Appl., 60 (2010), 2191-2199
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H.-N. Shi, J. Zhang, Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions, J. Inequal. Appl., 2013 (2013), 1-9
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]
Solvability of a fractional functional equation arising in some epidemic models
Solvability of a fractional functional equation arising in some epidemic models
en
en
We provide sufficient conditions for the existence of solutions to a fractional generalized Gripenberg equation, which arises
in the study of the spread of an infectious disease that does not induce permanent immunity.
1767
1785
Kishin
Sadarangani
Departamento de Matematicas
Universidad de Las Palmas de Gran Canaria
Spain
ksadaran@dma.ulpgc.es
Bessem
Samet
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Epidemic model
existence
solution
fractional order.
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]
Meir-Keeler theorem in b-rectangular metric spaces
Meir-Keeler theorem in b-rectangular metric spaces
en
en
In this paper, we prove a Meir-Keeler theorem in b-rectangular metric spaces. Thus, we answer the open question raised by
Ding et al. [H. S. Ding, V. Ozturk, S. Radenović, J. Nonlinear Sci. Appl., 8 (2015), 378–386].
1786
1790
Dingwei
Zheng
College of Mathematics and Information Science
Guangxi University
P. R. China
dwzheng@gxu.edu.cn
Pei
Wang
School of Mathematics and Information Science
Yulin Normal University
P. R. China
274958670@qq.com
Nada
Citakovic
Milirtary Academy
Serbia
nadac@list.ru
Fixed point
b-metric space
rectangular metric space
b-rectangular metric space.
Article.39.pdf
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[1]
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, (1980), 26-37
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H.-S. Ding, V. Ozturk, S. Radenović, On some new fixed point results in b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 378-386
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M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
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D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
]
Generalized hypergeometric k-functions via (k,s)-fractional calculus
Generalized hypergeometric k-functions via (k,s)-fractional calculus
en
en
We introduce (\(k; s\))-fractional integral operator involving (\(k, \tau\))-hypergeometric function and the Riemann-Liouville leftsided
and right-sided (\(k; s\))-fractional integral and differential operators. Then we present several useful and interesting results
involving the introduced operators. Also, the results presented here, being general, are pointed out to reduce to some known
results.
1791
1800
Kottakkaran Sooppy
Nisar
Department of Mathematics, College of Arts and Science at Wadi Al-dawaser
Prince Sattam bin Abdulaziz University
Kingdom of Saudi Arabia
ksnisar1@gmail.com
Gauhar
Rahman
Department of Mathematics
International Islamic University
Pakistan
gauhar55uom@gmail.com
Junesang
Choi
Department of Mathematics
Dongguk University
Republic of Korea
junesang@mail.dongguk.ac.kr
Shahid
Mubeen
Department of Mathematics
University of Sargodha
Pakistan
smjhanda@gmail.com
Muhammad
Arshad
Department of Mathematics
International Islamic University
Pakistan
marshad_zia@yahoo.com
Generalized hypergeometric function \(_pF_q\)
\(\tau\)-hypergeometric function
k-hypergeometric function
differential operators
(\(k، \tau\))-hypergeometric function
\(k\)-Pochhammer symbol
\(k\)-gamma function
\(k\)-beta function
(\(k،s\))-fractional integral.
Article.40.pdf
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M. Z. Sarikaya, Z. Dahmani, M. E. Kiris, F. Ahmad, (k, s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., 45 (2016), 77-89
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A. K. Shukla, J. C. Prajapati, On a generalized Mittag-Leffler type function and generated integral operator, Math. Sci. Res. J., 12 (2008), 283-290
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]
On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings
On the existence of coupled best proximity point and best proximity point for Suzuki type \(\alpha^+-\theta-\)proximal multivalued mappings
en
en
Following the study for the best proximity points of the Suzuki type \(\alpha^+-\theta\)-proximal single-valued mappings given by
Hussain et al., we deal with the Suzuki type \(\alpha^+-\theta\)-proximal multivalued mappings satisfying generalized conditions of existence,
some novel existence results of best proximity point and coupled best proximity points are established. Our results improve and
extend some recent results in the previous work.
1801
1819
Haiming
Liu
School of Mathematics
Mudanjiang Normal University
P. R. China
liuhm468@nenu.edu.cn
Xiaoming
Fan
School of Mathematical Sciences
Harbin Normal University
P. R. China
fanxm093@163.com
Lixu
Yan
Department of Mathematics
Harbin Institute of Technology
P. R. China
luckyyan1990@163.com
Zhigang
Wang
School of Mathematical Sciences
Harbin Normal University
P. R. China
wangzg2003205@163.com
Suzuki type \(\alpha^+-\theta\)-proximal multivalued mappings
coupled best proximity point
best proximity point.
Article.41.pdf
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N. Hussain, M. Hezarjaribi, M. A. Kutbi, P. Salimi, Best proximity results for Suzuki and convex type contractions, Fixed Point Theory Appl., 2016 (2016), 1-20
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M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
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Z.-G. Wang, H.-L. Li, Fixed point theorems and endpoint theorems for (\(\alpha,\psi\))-Meir-Keeler-Khan multivalued mappings, Fixed Point Theory Appl., 2016 (2016), 1-18
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K. Włodarczyk, R. Plebaniak, A. Banach, Best proximity points for cyclic and noncyclic set-valued relatively quasiasymptotic contractions in uniform spaces, Nonlinear Anal., 70 (2009), 3332-3341
]
Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral
Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral
en
en
In this paper, we are concerned with the existence of solutions for a second-order three-point nonlinear boundary value
problems involving the distributional Henstock-Kurzweil integral. By using the Leray-Schauder nonlinear alternative, we achieve
some results which are the generalizations of the previous results in the literatures.
1820
1829
Xuexiao
You
School of Mathematics and Statistics
College of Computer and Information
Hubei Normal University
Hohai University
P. R. China
P. R. China
youxuexiao@126.com
Wei
Liu
College of Science
Hohai University
P. R. China
liuw626@hhu.edu.cn
Guoju
Ye
College of Science
Hohai University
P. R. China
yegj@hhu.edu.cn
Dafang
Zhao
School of Mathematics and Statistics
College of Science, Hohai University, Nanjing, Jiangsu 210098, P. R. China
Hubei Normal University
P. R. China
dafangzhao@163.com
Distributional Henstock-Kurzweil integral
nonlinear boundary value problems
distributional derivative
Leray-Schauder nonlinear alternative.
Article.42.pdf
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S. Schwabik, G.-J. Ye, Topics in Banach space integration, Series in Real Analysis, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2005)
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Y.-P. Sun, L.-S. Liu, Solvability for a nonlinear second-order three-point boundary value problem, J. Math. Anal. Appl., 296 (2004), 265-275
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]
Exponential stability of neutral stochastic functional differential equations driven by G-Brownian motion
Exponential stability of neutral stochastic functional differential equations driven by G-Brownian motion
en
en
In this work, we study a class of neutral stochastic functional differential equations driven by G-Brownian motion. We
derive by variation-of-constants formula sufficient conditions for exponential stability and quasi sure exponential stability of the
solutions. Finally, we provide an example to illustrate the effectiveness of the theoretical results.
1830
1841
Min
Zhu
School of Mathematics and Statistics
College of Traffic Engineering
Central South University
Hunan University of Technology
China
China
zhumin0107@csu.edu.cn
Junping
Li
School of Mathematics and Statistics
Central South University
China
jpli@mail.csu.edu.cn
Yongxiang
Zhu
College of Traffic Engineering
Hunan University of Technology
China
zyx1998@sina.com
Neutral
variation-of-constants formula
exponential stability
G-Brownian motion.
Article.43.pdf
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W.-Y. Fei, C. Fei, On exponential stability for stochastic differential equations disturbed by G-Brownian motion, ArXiv, 2013 (2013), 1-19
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F.-Q. Gao, Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion, Stochastic Process. Appl., 119 (2009), 3356-3382
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S. Janković, J. Randjelovic, M. Janković, Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations, J. Math. Anal. Appl., 355 (2009), 811-820
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S.-G. Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stochastic Process. Appl., 118 (2008), 2223-2253
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]
Existence of homoclinic orbits for a higher order difference system
Existence of homoclinic orbits for a higher order difference system
en
en
By using critical point theory, some new criteria are obtained for the existence of a nontrivial homoclinic orbit to a higher
order difference system containing both many advances and retardations. The proof is based on the mountain pass lemma in
combination with periodic approximations. Related results in the literature are generalized and improved.
1842
1853
Xia
Liu
Oriental Science and Technology College
Science College
Hunan Agricultural University
Hunan Agricultural University
China
China
xia991002@163.com
Tao
Zhou
School of Business Administration
South China University of Technology
China
zhoutaoscut@hotmail.com
Haiping
Shi
Modern Business and Management Department
Guangdong Construction Polytechnic
China
shp7971@163.com
Homoclinic orbits
higher order difference systems
critical point theory
advances and retardations.
Article.44.pdf
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[1]
Z. Al-Sharawi (Ed.), J. M. Cushing (Ed.), S. Elaydi (Ed.), Theory and applications of difference equations and discrete dynamical systems, Proceedings of the International Conference on Difference Equations and Applications (ICDEA 2013) held at Sultan Qaboos University, Muscat, May 26–30, Springer Proceedings in Mathematics & Statistics, Springer, Heidelberg (2014)
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P. Chen, X.-H. Tang, Existence of homoclinic orbits for 2nth-order nonlinear difference equations containing both many advances and retardations, J. Math. Anal. Appl., 381 (2011), 485-505
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X.-Q. Deng, G. Cheng, H.-P. Shi, Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign, Comput. Math. Appl., 58 (2009), 1198-1206
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X.-Q. Deng, X. Liu, H.-P. Shi, T. Zhou, Homoclinic orbits for second order nonlinear p-Laplacian difference equations, translated from Izv. Nats. Akad. Nauk Armenii Mat., 46 (2011), 17–28, J. Contemp. Math. Anal., 46 (2011), 172-182
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X.-Q. Deng, X. Liu, Y.-B. Zhang, H.-P. Shi, Periodic and subharmonic solutions for a 2nth-order difference equation involving p-Laplacian, Indag. Math. (N.S.), 24 (2013), 613-625
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X.-Q. Deng, H.-P. Shi, X.-L. Xie, Periodic solutions of second order discrete Hamiltonian systems with potential indefinite in sign, Appl. Math. Comput., 218 (2011), 148-156
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C.-J. Guo, R. P. Agarwal, C.-J. Wang, D. O’Regan, The existence of homoclinic orbits for a class of first-order superquadratic Hamiltonian systems, Mem. Differ. Equ. Math. Phys., 61 (2014), 83-102
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C.-J. Guo, D. O’Regan, C.-J. Wang, R. P. Agarwal, Existence of homoclinic orbits of superquadratic second-order Hamiltonian systems, Z. Anal. Anwend., 34 (2015), 27-41
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X. Liu, Y.-B. Zhang, H.-P. Shi, Homoclinic orbits of second order nonlinear functional difference equations with Jacobi operators, Indag. Math. (N.S.), 26 (2015), 75-87
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Integral inequalities of the Hermite--Hadamard type for (\(\alpha,m\))-GA-convex functions
Integral inequalities of the Hermite--Hadamard type for (\(\alpha,m\))-GA-convex functions
en
en
In this paper, the authors introduce a notion “ (\(\alpha,m\))-GA-convex function” and establish some Hermite–Hadamard type
inequalities for this kind of convex functions.
1854
1860
Ye
Shuang
College of Mathematics
Inner Mongolia University for Nationalities
China
shuangye152300@sina.com
Feng
Qi
Institute of Mathematics
Department of Mathematics, College of Science
Henan Polytechnic University
Tianjin Polytechnic University
China
China
qifeng618@msn.com
Hermite–Hadamard type integral inequality
(\(\alpha،m\))-convex function
(\(\alpha،m\))-GA-convex function.
Article.45.pdf
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[1]
R.-F. Bai, F. Qi, B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and (\(\alpha,m\))-logarithmically convex functions, Filomat, 27 (2013), 1-7
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B.-Y. Xi, R.-F. Bai, F. Qi, Hermite-Hadamard type inequalities for the m- and (\(\alpha,m\))-geometrically convex functions, Aequationes Math., 84 (2012), 261-269
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B.-Y. Xi, F. Qi, Hermite-Hadamard type inequalities for geometrically r-convex functions, Studia Sci. Math. Hungar., 51 (2014), 530-546
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B.-Y. Xi, S.-H. Wang, F. Qi, Some inequalities for (h,m)-convex functions, J. Inequal. Appl., 2014 (2014), 1-12
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B.-Y. Xi, T.-Y. Zhang, F. Qi, Some inequalities of Hermite-Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357-361
]
Berge's maximum theorem to vector-valued functions with some applications
Berge's maximum theorem to vector-valued functions with some applications
en
en
In this paper, we introduce pseudocontinuity for Berge’s maximum theorem for vector-valued functions which is weaker
than semicontinuity. We prove the Berge’s maximum theorem for vector-valued functions with pseudocontinuity and obtain the
set-valued mapping of the solutions is upper semicontinuous with nonempty and compact values. As applications, we derive
some existence results for weakly Pareto-Nash equilibrium for multiobjective games and generalized multiobjective games both
with pseudocontinuous vector-valued payoffs. Moreover, we obtain the existence of essential components of the set of weakly
Pareto-Nash equilibrium for these discontinuous games in the uniform topological space of best-reply correspondences. Some
examples are given to investigate our results.
1861
1872
Qiu
Xiaoling
School of Mathematics and Statistics
Guizhou University
China
xlqiuzsy@163.com
Peng
Dingtao
School of Mathematics and Statistics
Guizhou University
China
dingtaopeng@126.com
Yu
Jian
School of Mathematics and Statistics
Guizhou University
China
Jyu1@gzu.edu.cn
Maximum theorem
vector-valued functions
set-valued mapping
pseudocontinuity
weakly Pareto-Nash equilibrium
essential components.
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]
Optimal tracking performance of discrete-time systems with quantization
Optimal tracking performance of discrete-time systems with quantization
en
en
This paper studies optimal tracking performance issues for linear time invariant system with two-channel constraints. The
specific problem under consideration is quantization for up-link and down-link communication channel which satisfies some
constraints. Logarithmic quantization law is employed in the quantizers. The tracking performance is defined in an square
sense, and the reference signal under consideration in this paper is a step signal. The system’s reference signal is considered
as a step signal. The tracking performance is measured by the minimum mean square error between the reference input and
the system’s output. By using dynamic programming approach, discrete-time algebraic Riccati equation (ARE) is obtained. The
optimal tracking performance is obtained by output feedback control, in terms of the space equation of the given system and the
unique solution of the discrete-time algebraic Riccati equation. And, the impact of quantizer for optimal tracking performance
is analyzed. Finally, simulation example is given to illustrate the theoretical results.
1873
1880
Chao-Yang
Chen
School of Information Science and Engineering
School of Information and Electrical Engineering
Central South University
Hunan University of Science and Technology
P. R. China
P. R. China
Weihua
Gui
School of Information Science and Engineering
Central South University
P. R. China
Shaowu
Zhou
School of Information and Electrical Engineering
Hunan University of Science and Technology
P. R. China
Zhi-Wei
Liu
College of Automation
Huazhong University of Science and Technology
P. R. China
Zhi-Hong
Guan
College of Automation
Huazhong University of Science and Technology
P. R. China
Ning
Gui
School of Information
Zhejiang Sci-Tech University
P. R. China
ninggui@gmail.com
Optimal tracking performance
quantization
two-channel constraints
discrete-time systems
algebraic Riccati equation (ARE).
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M. Ait Rami, X. Chen, X. Y. Zhou, Discrete-time indefinite LQ control with state and control dependent noises, Nonconvex optimization in control, J. Global Optim., 23 (2002), 245-265
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C.-Y. Chen, Z.-H. Guan, M. Chi, Y.-H. Wu, X.-W. Jiang, Fundamental performance limitations of networked control systems with novel trade-off factors and constraint channels, J. Franklin Inst., 354 (2017), 3120-3133
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C.-Y. Chen, B. Hu, Z.-H. Guan, M. Chi, D.-X. He, Optimal tracking performance of control systems with two-channel constraints, Inf. Sci., 374 (2016), 85-99
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X.-M. Chen, Z.-Y. Zhang, S.-L. Chen, Finite-signal-to-noise ratio diversity-multiplexing-rate trade-off in limited feedback beamforming systems with imperfect channel state information, IET Commun., 6 (2012), 751-758
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X. Cong, K. Shuang, S. Su, F.-C. Yang, An efficient server bandwidth costs decreased mechanism towards mobile devices in cloud-assisted P2P-VoD system, Peer-to-Peer Netw. Appl., 7 (2014), 175-187
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J.-W. Dong, W.-J. Kim, Bandwidth allocation and scheduling of networked control systems with exponential and quadratic approximations, Control Eng. Pract., 26 (2014), 72-81
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H. Fares, C. Langlais, Finite-signal-to-noise ratio diversity-multiplexing-delay tradeoff in half-duplex hybrid automatic repeat request relay channels, IET Commun., 9 (2015), 872-879
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M.-Y. Fu, L.-H. Xie, The sector bound approach to quantized feedback control, IEEE Trans. Automat. Control, 50 (2005), 1698-1711
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E. Garcia, P. J. Antsaklis, Model-based event-triggered control for systems with quantization and time-varying network delays, IEEE Trans. Automat. Control, 58 (2013), 422-434
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Z.-H. Guan, C.-Y. Chen, G. Feng, T. Li, Optimal tracking performance limitation of networked control systems with limited bandwidth and additive colored white Gaussian noise, IEEE Trans. Circuits Syst. I, Reg. Papers, 60 (2013), 189-198
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Y.-Q. Li, J. Chen, E. Tuncel, W.-Z. Su, MIMO control over additive white noise channels: stabilization and tracking by LTI controllers, IEEE Trans. Automat. Control, 61 (2016), 1281-1296
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F.-W. Li, X.-C. Wang, P. Shi, Robust quantized \(H_\infty\) control for network control systems with Markovian jumps and time delays, Int. J. Innov. Comput. I., 9 (2013), 4889-4902
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F. Mazenc, M. Malisoff, Trajectory based approach for the stability analysis of nonlinear systems with time delays, IEEE Trans. Automat. Control, 60 (2015), 1716-1721
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C. Peng, T. C. Yang, Event-triggered communication and \(H_\infty\) control co-design for networked control systems, Automatica J. IFAC, 49 (2013), 1326-1332
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T. Qi, W.-Z. Su, J. Chen, Tracking performance for output feedback control under quantization constraints, Proc. 30th Chinese Control Conf., Yantai, (2011), 6419-6424
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A. J. Rojas, Signal-to-noise ratio fundamental limitations in the discrete-time domain, Systems Control Lett., 61 (2012), 55-61
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E. I. Silva, G. C. Goodwin, D. E. Quevedo, Control system design subject to SNR constraints, Automatica J. IFAC, 46 (2010), 428-436
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L.-K. Sun, J.-G. Wu, Schedule and control co-design for networked control systems with bandwidth constraints, J. Franklin Inst., 351 (2014), 1042-1056
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B.-X. Wang, X.-W. Jiang, C.-Y. Chen, Trade-off performance analysis of LTI system with channel energy constraint, ISA Trans., 65 (2016), 88-95
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Y.-W. Wang, W. Yang, J.-W. Xiao, Z.-G. Zeng, Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., PP, (2016), 1560-1571
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L. Wei, M.-Y. Fu, H.-S. Zhang, Quantized output feedback control with multiplicative measurement noises, Internat. J. Robust Nonlinear Control, 25 (2015), 1338-1351
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X.-S. Zhan, J. Wu, T. Jiang, X.-W. Jiang, Optimal performance of networked control systems under the packet dropouts and channel noise, ISA Trans., 58 (2015), 214-221
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L.-X. Zhang, H.-J. Gao, O. Kaynak, Network-induced constraints in networked control systems–a survey, IEEE Trans. Ind. Informat., 9 (2016), 403-416
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H. Zhang, Y. Shi, A. S. Mehr, Robust \(H_\infty\) PID control for multivariable networked control systems with disturbance/noise attenuation, Internat. J. Robust Nonlinear Control, 22 (2012), 183-204
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X.-S. Zhao, Z.-H. Guan, F.-S. Yuan, X.-H. Zhang, Optimal performance of discrete-time control systems based on networkinduced delay, Eur. J. Control, 19 (2013), 37-41
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X.-W. Zhao, B. Hu, Z.-H. Guan, C.-Y. Chen, M. Chi, X.-H. Zhang, Multi-flocking of networked non-holonomic mobile robots with proximity graphs, IET Control Theory Appl., 10 (2016), 2093-2099
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Q. Zhou, P. Shi, S.-Y. Xu, H.-Y. Li, Observer-based adaptive neural network control for nonlinear stochastic systems with time delay, IEEE Trans. Neural Netw. Learn. Syst., 24 (2013), 71-80
]
Common coupled fixed point results in multiplicative metric spaces and applications
Common coupled fixed point results in multiplicative metric spaces and applications
en
en
In the framework of a multiplicative metric space, by using the concept of \(w^*\)-compatible mappings, we establish some new
common coupled fixed point theorems for two mappings satisfying \(\phi\)-type contractive condition. We do not use the condition
of continuity of any mapping for finding the coupled coincidence and common coupled fixed point. Meantime, we also provide
some examples to support our new results. As an application, we provide an existence and uniqueness theorem of common
solution for a class of nonlinear integral equations by using the obtained new result.
1881
1895
Yun
Jiang
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
1807862306@qq.com
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
gufeng99@sohu.com
Multiplicative metric spaces
coupled coincidence point
coupled common fixed point
\(w^*\)-compatible mapping pairs.
Article.48.pdf
[
[1]
M. Abbas, B. Ali, Y. I. Suleiman, Common fixed points of locally contractive mappings in multiplicative metric spaces with application, Int. J. Math. Math. Sci., 2015 (2015 ), 1-7
##[2]
M. Abbas, M. Ali Khan, S. Redenović, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
##[3]
M. Abbas, A. R. Khan, T. Nazir, Coupled common fixed point results in two generalized metric spaces, Appl. Math. Comput., 217 (2011), 6328-6336
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A. E. Bashirov, E. M. Kurpınar, A. Özyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48
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A. E. Bashirov, E. Mısırlı, Y. Tandoğdu, A. Özyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Ser. B, 26 (2012), 425-438
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Y. J. Cho, M. H. Shah, N. Hussain, Coupled fixed points of weakly F-contractive mappings in topological spaces, Appl. Math. Lett., 24 (2011), 1185-1190
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T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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F. Gu, Some new common coupled fixed point results in two generalized metric spaces, Fixed point Theory Appl., 2013 (2013), 1-21
##[9]
F. Gu. Y. J. Cho, Common fixed point results for four maps satisfying \(\phi\)-contractive condition in multiplicative metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-19
##[10]
F. Gu, L. Wang, Some coupled fixed-point theorems in two quasi-partial metric spaces, Fixed point Theory Appl., 2015 (2015 ), 1-17
##[11]
F. Gu, Y. Yin, A new common coupled fixed point theorem in generalized metric space and applications to integral equations, Fixed Point Theory Appl., 2013 (2013), 1-17
##[12]
F. Gu, S.-H. Zhou, Coupled common fixed point theorems for a pair of commuting mappings in partially ordered G-metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 1-18
##[13]
X.-J. He, M.-M. Song, D.-P. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed Point Theory Appl., 2013 (2013), 1-9
##[14]
E. Karapınar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59 (2010), 3656-3668
##[15]
V. Lakshmikantham, Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
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M. Özavşar, A. C. Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, ArXiv, 2012 (2012 ), 1-14
##[17]
B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 72 (2010), 4508-4517
##[18]
W. Shatanawi, On w-compatible mappings and common coupled coincidence point in cone metric spaces, Appl. Math. Lett., 25 (2012), 925-931
##[19]
W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling, 55 (2012), 680-687
]
Discrete-time projection neural network methods for computing the solution of variational inequalities
Discrete-time projection neural network methods for computing the solution of variational inequalities
en
en
Neural networks are useful tools to solve mathematical and engineering problems. By using the implicit-explicit-method and the method proposed recently by Mohamad to discretize the continuous-time neural networks, we formulate two classes of
discrete-time analogues to solve a system of variational inequalities. By adopting suitable Lyapunov functions and Razumikhintype
techniques, exponential stability of the discrete neural networks are established in terms of linear matrix inequalities (LMIs).
Several numerical experiments are performed to compare the convergence rates of the proposed discrete neural networks and it
is shown that:
(a) all of the discrete neural networks converge faster as the step size becomes larger,
(b) the discrete neural networks derived by the semi-implicit Euler method performs best.
1896
1907
Liping
Zhang
School of Science
Sichuan University of Science and Engineering
China
Shu-Lin
Wu
School of Science
Sichuan University of Science and Engineering
China
wushulin_ylp@163.com
Neural networks
linear matrix inequalities (LMIs)
variational inequalities
discretization.
Article.49.pdf
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]
A uniqueness result for final boundary value problem of microstretch bodies
A uniqueness result for final boundary value problem of microstretch bodies
en
en
Main subject of this study is the final boundary value problem of a microstretch thermoelastic body. In fact, using an
elementary transformation, this problem is reformulated as a known mixed problem with initial and boundary conditions.
We prove some results of uniqueness of solutions avoiding any conservation law of energy. We also give up any hypothesis
regarding the boundedness of the thermoelastic coefficients.
1908
1918
M.
Marin
Department of Mathematics and Computer Science
Transilvania University of Brasov
Romania
m.marin@unitbv.ro
D.
Baleanu
Department of Mathematics
nstitute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@cankaya.edu.tr
C.
Carstea
Department of Mathematics and Computer Science
Transilvania University of Brasov
Romania
R.
Ellahi
Department of Mathematics and Statistics
Department of Mechanical Engineering
FBAS, IIUI
University of California Riverside
Pakistan
USA
rellahi@engr.ucr.edu
Final boundary value problem
uniqueness of solution
microstretch
thermoelastic body.
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]
New stability conditions of neutral delay systems via free-matrix-based integral inequality
New stability conditions of neutral delay systems via free-matrix-based integral inequality
en
en
The problem of robust stability of uncertain neutral systems with time-delay is studied in this paper. A new free-matrixbased
integral inequality is proposed, which is more tighter than existing ones. By using it to investigate the stability of neutral
delay systems, less conservative stability conditions are obtained, which are presented in terms of linear matrix inequalities
(LMIs). Two numerical examples are provided to illustrate the effectiveness and the reduced conservativeness of the method.
1919
1926
Wei
Wang
School of Electrical and Information Engineering
Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province
Hunan University of Technology
China
China
wangwi9804@163.com
Hong-Bing
Zeng
School of Electrical and Information Engineering
Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province
Hunan University of Technology
China
China
9804zhb@163.com
Shen-Ping
Xiao
School of Electrical and Information Engineering
Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province
Hunan University of Technology
China
China
xsph_519@163.com
Gang
Chen
School of Electrical and Information Engineering
Hunan University of Technology
China
chengang@hut.edu.cn
Hong-Hai
Lian
School of Electrical and Information Engineering
Hunan University of Technology
China
1132830550@qq.com
Stability
neutral system
free-matrix-based integral inequality
Lyapunov-Krasovskii functional.
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H.-B. Zeng, Y. He, M. Wu, J.-H. She, Free-matrix-based integral inequality for stability analysis of systems with timevarying delay, IEEE Trans. Automat. Control, 60 (2015), 2768-2772
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C.-K. Zhang, Y. He, L. Jiang, M. Wu, An improved summation inequality to discrete-time systems with time-varying delay, Automatica J. IFAC, 74 (2016), 10-15
##[25]
C.-K. Zhang, Y. He, L. Jiang, M. Wu, H.-B. Zeng, Delay-variation-dependent stability of delayed discrete-time systems, IEEE Trans. Automat. Control, 61 (2016), 2663-2669
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C.-K. Zhang, Y. He, L. Jiang, M. Wu, H.-B. Zeng, Stability analysis of systems with time-varying delay via relaxed integral inequalities, Systems Control Lett., 92 (2016), 52-61
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X.-M. Zhang, M. Wu, J.-H. She, Y. He, Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica J. IFAC, 41 (2005), 1405-1412
]
New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control
New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control
en
en
This paper studies the problem of master-slave synchronization for uncertain Lur’e system via time-varying delayed feedback
control. It proves a new inequality involving double integrals, which can reduce the conservatism of the known Jensen’s
like inequalities according to our analysis. By employing this new inequality and a new class of novel mode-dependent augmented
Lyapunov-Krasovskii functional (LKF), it establishes some novel synchronization criteria, where the controller gain can
be achieved by solving a set of linear matrix inequalities (LMIs). Two examples with numerical simulations are given to illustrate
the feasibility and the superiority of our methods.
1927
1940
Yanmeng
Wang
College of Sciences
Nanjing University of Aeronautics and Astronautics
China
18213498367@163.com
Lianglin
Xiong
School of Mathematical Sciences
Yunnan Minzu University
China
lianglin-5318@163.com
Xinzhi
Liu
Department of Applied Mathematics
University of Waterloo Waterloo
Canada N2L 3G1
xinzhi.liu@uwaterloo.ca
Haiyang
Zhang
School of Science
Nanjing University of Science and Technology
China
Haiya287@126.com
Uncertain Lur’e system
synchronization
improved integral inequality
linear matrix inequalities.
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C. Ge, C.-C. Hua, X.-P. Guan, Master-slave synchronization criteria of Lur’e systems with time-delay feedback control, Appl. Math. Comput., 244 (2014), 895-902
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H.-M. Guo, S.-M. Zhong, Synchronization criteria of time-delay feedback control system with sector-bounded nonlinearity, Appl. Math. Comput., 191 (2007), 550-559
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Q.-L. Han, New delay-dependent synchronization criteria for Lur’e systems using time delay feedback control, Phys. Lett. A, 360 (2007), 563-569
##[8]
Y. He, G.-L. Wen, Q.-G. Wang, Delay-dependent synchronization criterion for Lure systems with delay feedback control, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), 3087-3091
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D. H. Ji, J. H. Park, S. C.Won, Master-slave synchronization of Lur’e systems with sector and slope restricted nonlinearities, Phys. Lett. A., 373 (2009), 1044-1050
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T. Li, J.-J. Yu, Z. Wang, Delay-range-dependent synchronization criterion for Lure systems with delay feedback control, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 1796-1803
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X.-X. Liao, G.-R. Chen, Chaos synchronization of general Lure systems via time-delay feedback control, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 207-220
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H. Mkaouar, O. Boubaker, Chaos synchronization for master slave piecewise linear systems: application to Chua’s circuit, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1292-1302
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A. Seuret, F. Gouaisbaut, Integral inequality for time-varying delay systems, European Control Conference (ECC 2013), Zurich, Switzerland, (2013), 1-6
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A. Seuret, F. Gouaisbaut, Integral inequality for time-varying delay systems, Automatica, 49 (2013), 2860-2866
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J. A. K. Suykens, J. Vandewalle, Master-slave synchronization of Lur’e systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 7 (1997), 665-669
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J.-W. Xia, J. H. Park, H.-B. Zeng, Improved delay-dependent robust stability analysis for neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays, Neurocomputing, 149 (2015), 1198-1205
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M. E. Yalcin, J. Suykens and J. Vandewalle, Masterslave synchronization of Lur’e systems with time-delay, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 11 (2001), 1707-1722
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X.-M. Zhang, M. Wu, J.-H. She, Y. He, Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica J. IFAC, 41 (2005), 1405-1412
]
Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach
Stability analysis of delayed Takagi-Sugeno fuzzy systems: a new integral inequality approach
en
en
This paper is concerned with the problem of the stability analysis for Takagi-Sugeno (T-S) fuzzy systems with interval
time-varying delay. The delay is assumed to be differential with interval bounds, and has both the lower and upper bounds
of the delay derivatives, in which the upper bound of delay derivative may be greater than one. By constructing some delaydependent
Lyapunov functions, some stability criteria are derived by using the convex optimization method and new integral
inequality techniques. Utilizing integral inequalities for quadratic functions plays a key role in the field of stability analysis for
delayed T-S fuzzy systems, and some integral inequalities for quadratic functions are derived and employed in order to produce
tighter bounds than what the Jensen inequality and Wirtinger-based inequality produce. Then, less conservative stability criteria
are derived by using convex combination method and improved integral inequalities based on appropriate Lyapunov-Krasovskii
(LK) functional. Finally, several examples are given to show the advantages of the proposed results.
1941
1959
Jiyao
An
College of Computer Science and Electronic Engineering
Hunan University
China
anbobcn@aliyun.com
Xinzhi
Liu
Department of Applied Mathematics
University of Waterloo
Canada N2L 3G1
xinzhi.liu@uwaterloo.ca
Guilin
Wen
State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, College of Mechanical and Vehicle Engineering
Hunan University
China
glwen@hnu.edu.cn
T-S fuzzy systems
stability
interval time-varying delay
integral inequality
Lyapunov-Krasovskii (LK) functional.
Article.53.pdf
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[1]
J.-Y. An, T. Li, G.-L. Wen, R.-F. Li, New stability conditions for uncertain TS fuzzy systems with interval time-varying delay, Int. J. Control Autom. Syst., 10 (2012), 490-497
##[2]
J.-Y. An, T. Li, G.-L. Wen, R.-F. Li, Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach, Fuzzy Sets and Systems, 185 (2011), 83-94
##[3]
J.-Y. An, G.-L. Wen, C. Lin, R.-F. Li, New results on delay-derivative- dependent fuzzy \(H^\infty\) filter design for T-S fuzzy systems, IEEE Trans. Fuzzy Syst., 19 (2011), 770-779
##[4]
J.-Y. An, G.-L. Wen, W. Xu, Improved results on fuzzy \(H_\infty\) filter design for T-S fuzzy systems, Discrete Dyn. Nat. Soc., 2010 (2010), 1-21
##[5]
C. Briat, Convergence and equivalence results for the Jensen’s inequality—application to time-delay and sampled-data systems, IEEE Trans. Automat. Control, 56 (2011), 1660-1665
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Y.-Y. Cao, P. M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 124 (2001), 213-229
##[7]
F. A. Faria, G. N. Silva, V. A. Oliverira, Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions, Internat. J. Systems Sci., 44 (2013), 1956-1969
##[8]
K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay systems, Control Engineering, Birkhäuser Boston, Inc., Boston, MA (2003)
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J. K. Hale, S. M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, Springer-Verlag, New York (1993)
##[10]
O. M. Kwon, M. J. Park, S. M. Lee, J. H. Park, Augmented Lyapunov-Krasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays, Fuzzy Sets and Systems, 201 (2012)
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D. H. Lee, Relaxed LMI conditions for local stability and local stabilization of continuous-time TakagiSugeno fuzzy systems, IEEE Trans. Cybern., 44 (2014), 394-405
##[12]
C.-H. Lien, K.-W. Yu, W.-D. Chen, Z.-L. Wan, Y.-J. Chung, Stability criteria for uncertain Takagi-Sugeno fuzzy systems with interval time-varying delay, IET Control Theory Appl., 1 (2007), 764-769
##[13]
F. Liu, M. Liu, Y. He, R. Yokoyama, New delay-dependent stability criteria for T-S fuzzy systems with time-varying delay, Fuzzy Sets and Systems., 161 (2010), 2033-2042
##[14]
Y. S. Moon, P. G. Park, W. H. Kwon, Y. S Lee, Delay-dependent robust stabilization of uncertain state-delayed systems, Internat. J. Control, 74 (2001), 1447-1455
##[15]
M. Narimani, H.-K. Lam, R. Dilmaghani, C. Wolfe, LMI-based stability analysis of fuzzy-model-based control systems using approximated polynomial membership functions, IEEE Trans. Syst., Man, Cybern. B, 41 (2011), 713-724
##[16]
P. G. Park, J. W. Ko, C.-K. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica J. IFAC, 47 (2011), 235-238
##[17]
P. G. Park, W. I. Lee, S. Y. Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, J. Franklin Inst., 352 (2015), 1378-1396
##[18]
C. Peng, M.-R. Fei , An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay, Fuzzy Sets and Systems, 212 (2013), 97-109
##[19]
C. Peng, M.-R. Fei, E.-G. Tian, Networked control for a class of T-S fuzzy systems with stochastic sensor faults, Fuzzy Sets and Systems, 212 (2013), 62-77
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C. Peng, Q.-L. Han, Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays, Inform. Sci., 181 (2011), 4287-4299
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C. Peng, L.-Y. Wen, J.-Q. Yang, On delay-dependent robust stability criteria for uncertain T-S fuzzy systems with interval time-varying delay, Int. J. Fuzzy Syst., 13 (2011), 35-44
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J.-B. Qiu, G. Feng, H.-J. Gao, Fuzzy-model-based piecewise \(H_\infty\) static-output-feedback controller design for networked nonlinear systems, IEEE Trans. Fuzzy Syst., 18 (2010), 919-934
##[23]
A. Seuret, F. Gouaisbaut, Wirtinger-based integral inequality: application to time-delay systems, Automatica J. IFAC, 49 (2013), 2860-2866
##[24]
A. Seuret, F. Gouaisbaut, Complete quadratic Lyapunov functionals using Bessel-Legendre inequality, Proceedings of European Control Conference, (2014), 448-453
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F. O. Souza, V. C. S. Campos, R. M. Palhares, On delay-dependent stability conditions for Takagi-Sugeno fuzzy systems, J. Franklin Inst., 351 (2014), 3707-3718
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T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern., 1 (1985), 116-132
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E.-G. Tian, D. Yue, Y.-J. Zhang, Delay-dependent robust \(H_\infty\) control for T-S fuzzy system with interval time-varying delay, Fuzzy Sets and Systems, 160 (2009), 1708-1719
##[28]
L.-G. Wu, X.-J. Su, P. Shi, J.-B. Qiu, A new approach to stability analysis and stabilization of discrete-time TS fuzzy time-varying delay systems, IEEE Trans. Syst., Man, Cybern. B, 41 (2011), 273-286
##[29]
X.-P. Xie, S.-L. Hu, Relaxed stability criteria for discrete-time TakagiSugeno fuzzy systems via new augmented nonquadratic Lyapunov functions, Neurocomputing, 166 (2015), 416-421
##[30]
X.-P. Xie, S.-X. Weng, H.-F. Zhang, Reducing the conservatism of stability analysis for discrete-time TS fuzzy systems based on a delayed Lyapunov function, Neurocomputing, 171 (2016), 1139-1145
##[31]
J. Yang, W.-P. Luo, K.-B. Shi, X. Zhao, Robust stability analysis of uncertain T-S fuzzy systems with time-varying delay by improved delay-partitioning approach, J. Nonlinear Sci. Appl., 9 (2016), 171-185
##[32]
H.-B. Zeng, J. H. Park, J.-W. Xia, S.-P. Xiao, Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay, Appl. Math. Comput., 235 (2014), 492-501
##[33]
X.-M. Zhang, Q.-L. Han, Novel delay-derivative-dependent stability criteria using new bounding techniques, Internat. J. Robust Nonlinear Control, 23 (2013), 1419-1432
##[34]
Z.-Y. Zhang, C. Lin, B. Chen, New stability and stabilization conditions for T-S fuzzy systems with time delay, Fuzzy Sets and Systems, 263 (2015), 82-91
]
Multiple periodic solutions for delay differential equations with a general piecewise constant argument
Multiple periodic solutions for delay differential equations with a general piecewise constant argument
en
en
This paper is concerned with the existence of multiple periodic solutions for some delay differential equations with a
general piecewise constant argument. Under some sufficient conditions, we establish the existence of two and three nonnegative
periodic solutions for the addressed delay differential equation with piecewise constant argument. Also, we apply one of our
main results to a Nicholson’s blowflies type model.
1960
1970
Hui-Sheng
Ding
College of Mathematics and Information Science
Jiangxi Normal University
P. R. China
dinghs@mail.ustc.edu.cn
Hong
Wang
College of Mathematics and Information Science
Jiangxi Normal University
P. R. China
1394007574@qq.com
Gaston M.
N'Guérékata
Department of Mathematics
Morgan State University
USA
Gaston.N’Guerekata@morgan.edu
Piecewise constant
periodic solution
multiple periodic solution.
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Generalizations of Hu-type inequalities and their applications
Generalizations of Hu-type inequalities and their applications
en
en
In this paper, we present some new generalizations of Hu-type inequalities, and then we obtain some new generalizations
and refinements of Hölder’s inequality.
1971
1985
Jingfeng
Tian
College of Science and Technology
North China Electric Power University
P. R. China
tianjf@ncepu.edu.cn
Zhen-Hang
Yang
Customer Service Center
State Grid Zhejiang Electric Power Research Institute
P. R. China
yzhkm@163.com
Hölder’s inequality
Hu-type inequality
generalization
refinement.
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Some new fuzzy fixed point theorems via distance functions with applications
Some new fuzzy fixed point theorems via distance functions with applications
en
en
In this paper, we prove some new fuzzy fixed point theorems on a space of fuzzy sets under a G-distance function and a
\(\acute{G}\)-distance function. Our results extend, generalize, and improve some existing results. Moreover, some applications are given
here to illustrate the usability of the obtained results.
1986
2000
Bitao
Cheng
School of Mathematics and Statistics
School of Mathematics and Statistics
Institute of Applied Mathematics
Qujing Normal University
Central South University
Qujing Normal University
P. R. China
P. R. China
P. R. China
chengbitao@126.com
Jianhua
Chen
School of Mathematics and Statistics
Central South University
P. R. China
cjh19881129@163.com
Xianhua
Tang
School of Mathematics and Statistics
Central South University
P. R. China
tangxh@mail.csu.edu.cn
Fuzzy set
fuzzy-mapping
G-distance functions
\(\acute{G}\)-distance functions
fuzzy fixed point.
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Lyapunov type equation for discrete exponential trichotomies
Lyapunov type equation for discrete exponential trichotomies
en
en
For a nonautonomous dynamics obtained by a sequence of linear operators acting on an arbitrary Hilbert space, we give a
complete characterization of the notion of a uniform exponential trichotomy in terms of what can be considered to be a discrete
version of the Lyapunov equation. We then use this characterization to study the stability of exponential trichotomies under
small linear and nonlinear perturbations.
2001
2017
Davor
Dragičević
School of Mathematics and Statistics
University of New South Wales
Australia
d.dragicevic@unsw.edu.au
Exponential trichotomies
robustness
perturbations.
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Composite relaxed extragradient method for triple hierarchical variational inequalities with constraints of systems of variational inequalities
Composite relaxed extragradient method for triple hierarchical variational inequalities with constraints of systems of variational inequalities
en
en
In this paper, we introduce and analyze a composite relaxed extragradient viscosity algorithm for solving the triple hierarchical
variational inequality problem with the constraint of general system of variational inequalities in a real Hilbert space.
Strong convergence of the iteration sequences generated by the algorithm is established under some suitable conditions. Our
results improve and extend the corresponding results in the earlier and recent literature.
2018
2039
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University; and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for General Education; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Composite relaxed extragradient algorithm
triple hierarchical variational inequality
general system of variational inequalities
inverse-strongly monotone mapping.
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]
Event-triggered \(H\infty\) controller design for networked Takagi-Sugeno systems with uncertainties and time delay
Event-triggered \(H\infty\) controller design for networked Takagi-Sugeno systems with uncertainties and time delay
en
en
This paper considers an event-triggered communication scheme for a class of networked Takagi-Sugeno (T-S) fuzzy systems
with uncertainties and time delay. By the parallel distributed compensation fuzzy control rules, a new type of closed-loop
nonlinear networked control systems (NCSs) with an interval time delay, uncertainties and event-triggered communication
strategy is modeled as a class of networked T-S fuzzy systems. In order to deal with the integral items and convert the coupling
time-varying matrix inequalities into a class of decoupling matrix inequalities, a new delay-dependent stabilization criterion
is presented firstly. Secondly, some novel criteria for the asymptotic stability analysis and control synthesis of event-triggered
networked T-S fuzzy systems with time delay and uncertainties are established in terms of linear matrix inequalities (LMIs).
Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
2040
2051
Huaicheng
Yan
School of Automation
Key Laboratory of Advanced Control and Optimization for Chemical Process of Ministry of Education
Hangzhou Dianzi University
East China University of Science and Technology
China
China
hcyan@ecust.edu.cn
Yuwei
Zhao
Key Laboratory of Advanced Control and Optimization for Chemical Process of Ministry of Education
East China University of Science and Technology
China
zywecust@163.com
Yun
Chen
School of Automation
Hangzhou Dianzi University
China
cloudscy@hdu.edu.cn
Shiming
Chen
School of Electrical and Electrical Engineering
East China Jiaotong University
China
shmchen@ecjtu.jx.cn
Xisheng
Zhan
College of Mechatronics and Control Engineering
Hubei Normal University
China
xisheng519@126.com
Event-triggered communication scheme
T-S fuzzy systems
time delay
uncertainties.
Article.59.pdf
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##[30]
H. Zhang, X.-Y. Zheng, H.-C. Yan, C. Peng, Z.-P. Wang, Q.-Y. Chen, Codesign of event-triggered and distributed \(H_\infty\) filtering for active semi-vehicle suspension systems, IEEE/ASME Trans. Mechatronics, 22 (2016), 1047-1058
]
Some results for common fixed point on $\varphi$-contractions in k-partially ordered fuzzy metric space
Some results for common fixed point on $\varphi$-contractions in k-partially ordered fuzzy metric space
en
en
The notion of coincidence point and common fixed point were extended in generalized partially ordered fuzzy metric
spaces. Under some conditions, some coincidence point and common fixed point theorems were established in generalized
partially fuzzy metric spaces using weakly compatible mappings. These results improve some theorems in corresponding
literature.
2052
2065
Jiaming
Jin
Department of Mathematics
Nanchang University
P. R. China
jiamingjin123@163.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Zhaoqi
Wu
Department of Mathematics
Nanchang University
P. R. China
Haochen
Wu
Department of Mathematics
Nanchang University
P. R. China
Fuzzy metric space
weakly compatible mappings
common fixed point
k-partially ordered.
Article.60.pdf
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[1]
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]
A new fixed point result via property P with an application
A new fixed point result via property P with an application
en
en
The purpose of this paper is to introduce a new contractive condition. We prove the existence and uniqueness of a fixed
point of self-mapping under this new contractive condition. Moreover, we observe analog of these results for the mappings that
satisfy the property P. An application on integral equations is presented to illustrate the main result. Our results extend and
generalize well-known results in the literature.
2066
2078
Z.
Mustafa
Department of Mathematics, Statistics and Physics
Department of Mathematics
Qatar University
The Hashemite University
Qatar
Jordan
zead@qu.edu.qa
M. M. M.
Jaradat
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
mmjst4@qu.edu.qa
E.
Karapinar
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
Department of Mathematics
Atilim University 06836
Saudi Arabia
Turkey
erdalkarapinar@yahoo.com
Contractive mapping
fixed point
partial metric space
property P
integral equations.
Article.61.pdf
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H. Aydi, E. Karapınar, A Meir-Keeler common type fixed point theorem on partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-10
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H. Aydi, E. Karapınar, New Meir-Keeler type tripled fixed-point theorems on ordered partial metric spaces, Math. Probl. Eng., 2012 (2012), 1-17
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H. Aydi, E. Karapınar, P. Kumam, A note on ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210’, J. Inequal. Appl., 2013 (2013), 1-3
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E. Karapınar, I. M. Erhan, Cyclic contractions and fixed point theorems, Filomat, 26 (2012), 777-782
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E. Karapınar, I. M. Erhan, A. Öztürk, Fixed point theorems on quasi-partial metric spaces, Math. Comput. Modelling, 57 (2013), 2442-2448
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]
Asymptotic behavior of non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps
Asymptotic behavior of non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps
en
en
In this paper, a non-autonomous stochastic Gilpin-Ayala predator-prey model with jumps is studied. Firstly, we show
that this model has a unique global positive solution under certain conditions. Then, we discuss the sufficient conditions for
stochastically ultimate boundedness and obtain the asymptotic behavior of the solution. Finally, sufficient criteria for extinction
of all prey and predator species, stochastic weak persistence in the mean of prey species are established.
2079
2093
Yanhua
Zhang
Institute of Oceanology, Chinese Academy of Sciences
University of Chinese Academy of Sciences
College of Science
China University of Petroleum
China
China
China
ggxpzyh@163.com
Gilpin-Ayala predator-prey model
jumps
moment boundedness
asymptotic behavior
extinction.
Article.62.pdf
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Positive properties of the Green function for two-term fractional differential equations and its application
Positive properties of the Green function for two-term fractional differential equations and its application
en
en
In this paper, we study the positive properties of the Green function for the following two-term fractional differential
equation \[
\begin{cases}
-D^\alpha_{0^+}u(t)+bu(t)=f(t,u(t)),\,\,\,\,\, 0<t<1,\\
u(0)=0,\,\,\,\,\, u(1)=0,
\end{cases}
\]
where \(1 < \alpha < 2, b > 0, D^\alpha_{0^+}\) is the standard Riemann-Liouville derivative. As an application, the existence and uniqueness of
positive solution are obtained under the singular conditions. Moreover, an iterative scheme is established to approximate the
unique positive solution.
2094
2102
Yongqing
Wang
School of Statistics
School of Mathematical Sciences
Qufu Normal University
Qufu Normal University
P. R. China
P. R. China
wyqing9801@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
P. R. China
Australia
lls@mail.qfnu.edu.cn
Multi-term fractional differential equation
Green function
iterative solution
boundary value problems.
Article.63.pdf
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]
Projective reduce order synchronization of fractional order chaotic systems with unknown parameters
Projective reduce order synchronization of fractional order chaotic systems with unknown parameters
en
en
This paper, mainly concerns the adaptive projective reduce order synchronization behavior of uncertain chaotic system.
By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two
chaotic and hyperchaotic systems asymptotically synchronized up to a desired identical and different scaling matrix. Numerical
simulation results show that the proposed method is effective, convenient, and also faster for projective dual synchronization of
chaotic and hyperchaotic systems.
2103
2114
M. Mossa
Al-sawalha
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia.
sawalha_moh@yahoo.com
Projective
reduce order synchronization
adaptive control
unknown parameters
Lyapunov stability theory.
Article.64.pdf
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P. Zhou, R.-J. Bai, The adaptive synchronization of fractional-order chaotic system with fractional-order 1 < q < 2 via linear parameter update law, Nonlinear Dynam., 80 (2015), 753-765
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]
A cooperative coevolution PSO technique for complex bilevel programming problems and application to watershed water trading decision making problems
A cooperative coevolution PSO technique for complex bilevel programming problems and application to watershed water trading decision making problems
en
en
The complex bilevel programming problem (CBLP) in this paper mainly refers to the optimistic BLP in which the highdimensional
decision variables at both levels. A cooperative coevolutionary particle swarm optimization (CCPSO) is proposed
for solving the (CBLP), in which the evolutionary paradigm can efficiently prevent the premature convergence of the swarm.
Furthermore, the stagnation detection strategy in our algorithm can further accelerate the convergence speed. Finally, we use the
test problems from the reference and practical example about watershed water trading decision-making problem to measure and
evaluate the proposed algorithm. The presented results indicate that the proposed algorithm can effectively solve the complex
bilevel programming problems.
2115
2132
Tao
Zhang
School of Information and Mathematics
Yangtze University
China
zt_math981@126.com
Zhong
Chen
School of Information and Mathematics
Yangtze University
China
Jiawei
Chen
School of Mathematics and Statistics
Southwest University
China
j.w.chen713@163.com
Complex bilevel programming
cooperative coevolutionary particle swarm optimization
watershed water trading decision making problems
elite strategy.
Article.65.pdf
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]
The Cauchy problems for discontinuous fuzzy systems under generalized differentiability
The Cauchy problems for discontinuous fuzzy systems under generalized differentiability
en
en
In this paper, we provide some existence theorems of generalized solutions to initial value problems for the discontinuous
fuzzy differential equations and the retarded fuzzy functional differential equations by using properties of strong fuzzy Henstock
integrals under strong GH-differentiability.
2133
2143
Qiang
Ma
Network Information Management Center
Northwest University for Nationalities
P. R. China
mq@xbmu.edu.cn
Ya-Bin
Shao
School of Science
Chongqing University of Posts and Telecommunications
P. R. China
yb-shao@163.com
Zeng-Tai
Gong
College of Mathematics and Statistics
Northwest Normal University
P. R. China
Fuzzy number
strong fuzzy Henstock integral
fuzzy differential equations
fuzzy retarded functional differential equations
fuzzy generalized solution.
Article.66.pdf
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]
The existence of infinitely many solutions for nonlinear elliptic equations involving p-Laplace type operators in \(\mathbb{R}^N\)
The existence of infinitely many solutions for nonlinear elliptic equations involving p-Laplace type operators in \(\mathbb{R}^N\)
en
en
We are concerned with the following nonlinear elliptic equations
\[-div(\varphi(x,\nabla u))+b(x)|u|^{p-2}u=\lambda f(x,u) \qquad \texttt{in} \qquad\mathbb{R}^N, \]
where the function \(\varphi(x,v)\) is of type \(|v|^{p-2}v, b:\mathbb{R}^N\rightarrow (0,\infty)\) is a continuous potential function, \(\lambda\) is a real parameter, and
\(f:\mathbb{R}^N\times \mathbb{R}\rightarrow\mathbb{R}\) is a Carath´eodory function. In this paper, under suitable assumptions, we show the existence of infinitely
many weak solutions for the problem above without assuming the Ambrosetti and Rabinowitz condition, by using the fountain
theorem. Next, we give a result on the existence of a sequence of solutions for the problem above converging to zero in the
\(L^\infty\)-norm by employing the Moser iteration under appropriate conditions.
2144
2161
Yun-Ho
Kim
Department of Mathematics Education
Sangmyung University
Republic of Korea
kyh1213@smu.ac.kr
Jung-Hyun
Bae
Department of Mathematics
Sungkyunkwan University
Republic of Korea
hoi1000sa@skku.edu
Jongrak
Lee
Institute of Mathematical Sciences
Ewha Womans University
Republic of Korea
jrlee0124@ewha.ac.kr
p-Laplace type
weak solution
iteration method
fountain theorem.
Article.67.pdf
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]
Model and algorithm for bilevel linear programming with fuzzy decision variables and multiple followers
Model and algorithm for bilevel linear programming with fuzzy decision variables and multiple followers
en
en
The bilevel linear programming with fuzzy decision variables and multiple followers model (MFFVBLP) is firstly established
and investigated, and the model optimal solution is shown to be equivalent to the optimal solution of the bilevel linear
programming with multiple followers by using fuzzy structured element theory in this paper. The optimal solution of this
model is found out by adopting the Kuhn-Tucker approach. An illustrative example is provided to demonstrate the feasibility
and efficiency of the proposed method for solving the MFFVBLP model.
2162
2170
Shengyue
Deng
School of Science
Department of Mathematics and Computational Science
Hunan University of Technology
Xiangtan University
P. R. China
P. R. China
dsy110@163.com
Jintao
Tan
School of Science
Hunan University of Technology
P. R. China
jeanette0219@163.com
Chengjie
Xu
School of Science
Hunan University of Technology
P. R. China
xu-chengjie@163.com
Xinfan
Wang
School of Science
Hunan University of Technology
P. R. China
zzwxfydm@126.com
Bilevel linear programming
fuzzy decision variables
multiple followers
fuzzy structured element.
Article.68.pdf
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S. Dempe, Foundations of bilevel programming, Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Dordrecht (2002)
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S.-Y. Deng, L.-Q. Zhou, X.-F. Wang, Bi-level multiple followers linear programming with upper constraint and fuzzy decision variables, Control Decis., 29 (2014), 1803-1808
##[4]
S.-Y. Deng, L.-Q. Zhou, X.-F. Wang, Solving the fuzzy bilevel linear programming with multiple followers through structured element method, Math. Probl. Eng., 2014 (2014), 1-6
##[5]
Y. Gao, G. Zhang, J. Ma, J. Lu, A \(\lambda\)-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization, IEEE Trans. Fuzzy Syst., 18 (2010), 1-13
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H. A. Gil, F. D. Galiana, E. L. Da Silva, Nodal price control: a mechanism for transmission network cost allocation, IEEE Trans. Power Syst., 21 (2006), 3-10
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S.-Z. Guo, Principle of fuzzy mathematical analysis based on structured element, Northeast University Press, Shenyang, China (2004)
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S.-Z. Guo, Comparison and ordering of fuzzy numbers based on method of structured element, Syst. Eng. Theory Pract., 29 (2009), 106-111
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K. Kogan, C. S. Tapiero, Optimal co-investment in supply chain infrastructure, European J. Oper. Res., 192 (2009), 265-276
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J. Lu, G.-Q. Zhang, T. Dillon, Fuzzy multi-objective bilevel decision making by an approximation Kth-best approach, J. Mult.-Valued Logic Soft Comput., 14 (2008), 205-232
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M. Sakawa, H. Katagiri, T. Matsui, Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility, Fuzzy Sets and Systems, 188 (2012), 45-57
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M. Sakawa, I. Nishizaki, Interactive fuzzy programming for decentralized two-level linear programming problems, Theme: decision and optimization, Fuzzy Sets and Systems, 125 (2002), 301-315
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M. Sakawa, I. Nishizaki, Interactive fuzzy programming for two-level linear fractional programming problems, Optimization and decision, Fuzzy Sets and Systems, 119 (2001), 31-40
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Z. Yao, S. C. H. Leung, K. K. Lai, Manufacturer’s revenue-sharing contract and retail competition, European J. Oper. Res., 186 (2008), 637-651
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G.-Q. Zhang, J. Lu, Y. Gao, An algorithm for fuzzy multi-objective multi-follower partial cooperative bilevel programming, J. Intell. Fuzzy Syst., 19 (2008), 303-319
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]
Anti-periodic solutions for BAM-type Cohen-Grossberg neural networks with time delays
Anti-periodic solutions for BAM-type Cohen-Grossberg neural networks with time delays
en
en
In this paper, a class of BAM-type Cohen-Grossberg neural networks with time delays are considered. Some sufficient
conditions for the existence and exponential stability of anti-periodic solutions are established.
2171
2180
Ping
Cui
Institute of Applied Mathematics, School of Teacher Education
Qujing Normal University
China
2008pingc@163.com
Zheng-Biao
Li
School of Mathematics and Statistics
Qujing Normal University
China
2991726233@qq.com
BAM Cohen-Grossberg neural networks
time delay
anti-periodic solution
exponential stability.
Article.69.pdf
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F.-J. Qin, X.-J. Yao, Existence and exponential stability of the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays, (Chinese) Comput. Eng. Softw., 5 (2014), 17-24
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]
On generalized solutions for discontinuous fuzzy differential equations and strong fuzzy Henstock integrals
On generalized solutions for discontinuous fuzzy differential equations and strong fuzzy Henstock integrals
en
en
In this paper, under the notion of strong uniformly \(AC^\nabla\) of fuzzy-number-valued functions, we prove a generalized controlled
convergence theorem of strong fuzzy Henstock integral. As the applications of this convergence theorem, we provide
sufficient conditions which guarantee the existence of generalized solutions to initial value problems for the fuzzy differential
equations by using properties of strong fuzzy Henstock integrals under strong GH-differentiability. In comparison with some
previous works, we consider equations whose right-hand side functions are not integrable in the sense of Kaleva on certain
intervals and their solutions are not absolute continuous functions.
2181
2195
Ya-Bin
Shao
School of Science
Chongqing University of Posts and Telecommunications
P. R. China
yb-shao@163.com
Zeng-Tai
Gong
College of Mathematics and Statistics
Northwest Normal University
P. R. China
zt-gong@163.com
Zi-Zhong
Chen
College of Computer Science and Technology
Chongqing University of Posts and Telecommunications
P. R. China
chenzz@cqupt.edu.cn
Fuzzy number
strong fuzzy Henstock integral
generalized controlled convergence theorem
fuzzy differential equations
generalized solution.
Article.70.pdf
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[1]
R. Alikhani, F. Bahrami, Global solutions of fuzzy integro-differential equations under generalized differentiability by the method of upper and lower solutions, Inform. Sci., 295 (2015), 600-608
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Novel delay-dependent robust stability criteria for neutral-type time-varying uncertain Lurie nonlinear control system with mixed time delays
Novel delay-dependent robust stability criteria for neutral-type time-varying uncertain Lurie nonlinear control system with mixed time delays
en
en
This study examines the problem of robust stability analysis of neutral-type time-varying uncertain Lurie nonlinear control
system with mixed time delays. Firstly, by discretizing the time-delay interval into non-uniformly multiple subintervals
and decomposing the corresponding integral intervals to estimate the bounds of integral terms more exactly, less conservative
stability criteria are derived. Secondly, based on the above delay-partitioning method, a newly augmented Lyapunov-Krasovkii
functional is constructed. Thirdly, by taking full advantage of Wirtinger’s integral inequality, which can provide tighter upper
bound than Jensen’s inequality, novel delay-dependent robust stability conditions are obtained in terms of linear matrix inequalities.
Finally, several numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results.
2196
2213
Kaibo
Shi
School of Information Science and Engineering
Chengdu University
China
Youhua
Wei
College of Geophysics, Geomathematics Key Laboratory of Sichuan Province
Chengdu University of Technology
China
weiyouhua@cdut.cn
Shouming
Zhong
School of Mathematics Sciences
University of Electronic Science and Technology of China
China
Jun
Wang
College of Electrical and Information Engineering
Southwest University for Nationalities
China
Lurie nonlinear control system
mixed time-varying delays
Wirtinger’s integral inequality
Lyapunov-Krasovkii functional
linear matrix inequality.
Article.71.pdf
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]
Hybrid iterative algorithms for the split common fixed point problems
Hybrid iterative algorithms for the split common fixed point problems
en
en
In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) based on the
hybrid steepest descent method for solving the split common fixed point problems. We establish the strong convergence of
the sequences generated by the proposed algorithms to a solution of the split common fixed point problems, which is also a
solution of a certain variational inequality. In particular, the minimum norm solution of the split common fixed point problems
is obtained. As applications, variational problems and equilibrium problems are considered.
2214
2228
Jong Soo
Jung
Department of Mathematics
Dong-A University
Korea
jungjs@dau.ac.kr
Split common fixed point problem
firmly nonexpansive mapping
nonexpansive mapping
variational inequality
minimum-norm
bounded linear operator
variational problems
equilibrium problems
iterative algorithms.
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Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense
Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense
en
en
In this work, we study fixed points of nonself-mappings which are asymptotically pseudocontractive in the intermediate
sense via an implicit iterative process. Convergence analysis is investigated in the framework of Hilbert spaces. We also give
strong convergence criteria for the class of mappings.
2229
2240
Yunpeng
Zhang
College of Electric Power
North China University of Water Resources and Electric Power
China
zhangypliyl@yeah.net
Asymptotically pseducontractive mapping
implicit algorithm
metric projection
convergence analysis.
Article.73.pdf
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Stability of random implicit multifunctions in separable Asplund spaces
Stability of random implicit multifunctions in separable Asplund spaces
en
en
This paper is mainly devoted to present new sufficient conditions in terms of Fr´echet coderivatives for the local metric
regularity, the metric regularity, the Lipschitz-like property, the nonemptiness and the lower semicontinuity of random implicit
multifunctions in separable Asplund spaces. An example is given to illustrate the above random implicit multifunction results.
Some applications to stability analysis of solution maps for random parametric generalized equations are also given.
2241
2256
Ming-ge
Yang
School of Management
Shanghai University
P. R. China
mgyang@t.shu.edu.cn
Yi-fan
Xu
School of Management
Fudan University
P. R. China
yfxu@fudan.edu.cn
Fréchet coderivative
random implicit multifunction
(local) metric regularity
Lipschitz-like property
lower semicontinuity.
Article.74.pdf
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Maximum principles for time-fractional Caputo-Katugampola diffusion equations
Maximum principles for time-fractional Caputo-Katugampola diffusion equations
en
en
Maximum and minimum principles for time-fractional Caputo-Katugampola diffusion operators are proposed in this paper.
Several inequalities are proved at extreme points. Uniqueness and continuous dependence of solutions for fractional diffusion
equations of initial-boundary value problems are considered.
2257
2267
Liang
Cao
School of Automation
Guangdong University of Technology
P. R. China
bdhzxcaoliang@163.com
Hua
Kong
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science
Neijiang Normal University
P. R. China
konghua2008@126.com
Sheng-Da
Zeng
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science
Institute of Computer Science, Faculty of Mathematics and Computer Science
Neijiang Normal University
Jagiellonian University
P. R. China
Poland
shdzeng@hotmail.com;zengshengda@163.com
Caputo-Katugampola fractional operators
fractional diffusion equations
maximum principles
uniqueness
continuous dependence.
Article.75.pdf
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]
Noether theory for Birkhoffian systems with nabla derivatives
Noether theory for Birkhoffian systems with nabla derivatives
en
en
There are discrete phenomena which happen only on discrete time or hold discrete space structures such as economy series,
population dynamics et al.. Then there is a tool needed for these discrete issues or applications. Time scale is one of the useful
tools to solve some discrete problems. In this paper, time scale is used to establish discrete Pfaff-Birkhoff principle and achieve
discrete Birkhoff equations, discrete Noether identity and discrete conserved quantity for the discrete Birkhoffian system. Firstly,
Birkhoff equations, Noether identity and Noether theorem with nabla derivatives on time scales are investigated by using the
isochronous variational principle. Secondly, some special cases, especially the discrete Birkhoffian system are discussed. Thirdly,
another method, i.e., the duality principle is introduced for the Birkhoffian system on time scales. And finally, an example is
given to illustrate the results and methods.
2268
2282
Chuanjing
Song
College of Science
Nanjing University of Science and Technology
P. R. China
songchuanjingsun@126.com
Yi
Zhang
College of Civil Engineering
Suzhou University of Science and Technology
P. R. China
zhy@mail.usts.edu.cn
Noether theorem
Birkhoffian system
time scale
duality principle
isochronous variational principle.
Article.76.pdf
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]