]>
2017
10
8
ISSN 2008-1898
505
Fixed point theorems in modular vector spaces
Fixed point theorems in modular vector spaces
en
en
In this work, we initiate the metric fixed point theory in modular vector spaces under Nakano formulation. In particular, we
establish an analogue to Banach contraction principle, Browder and G¨ohde fixed point theorems for nonexpansive mappings in
the modular sense. Then we finish by proving a common fixed point result of a commutative family of nonexpansive mappings
in the modular sense.
4046
4057
Afrah A. N.
Abdou
Department of Mathematics, Faculty of Sciences
King Abdulaziz University
Saudi Arabia
aabdou@kau.edu.sa
Mohamed A.
Khamsi
Department of Mathematical Sciences
Department of Mathematics & Statistics
The University of Texas at El Paso
King Fahd University of Petroleum and Minerals
U.S.A
Saudi Arabia
mohamed@utep.edu
Best approximant
electrorheological fluids
fixed point
modular vector spaces
Nakano
nonexpansive
uniformly convex.
Article.1.pdf
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]
Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix
Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix
en
en
In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are `` similar'' to the Toeplitz matrices. Their (-1,-1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (-1, 1)-circulants and (1, -1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.
4058
4070
Xiaoyu
Jiang
Department of Information and Telecommunications Engineering
The University of Suwon
Korea
jxy19890422@sina.com
Kicheon
Hong
Department of Information and Telecommunications Engineering
The University of Suwon
Korea
Kchong@suwon.ac.kr
Zunwei
Fu
Department of Mathematics
The University of Suwon, Wau-ri
Korea
zwfu@mail.bnu.edu.cn
CUML Toeplitz matrix
CUML Hankel matrix
skew cyclic displacement
RSFPLR circulants
RFMLR circulants
decomposition
inverse.
Article.2.pdf
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]
On approximate homomorphisms of ternary semigroups
On approximate homomorphisms of ternary semigroups
en
en
We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into \(n\)-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and \(p\)-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists for their research in some problems coming from quantum physics, \(p\)-adic strings and superstrings.
4071
4076
Krzysztof
Ciepliński
Faculty of Applied Mathematics
AGH University of Science and Technology
Poland
cieplin@agh.edu.pl
Ulam stability
(commutative) ternary semigroup
ternary homomorphism
n-Banach space
(complete) non-Archimedean normed space
p-adic numbers.
Article.3.pdf
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]
On the generalized solutions of a certain fourth order Euler equations
On the generalized solutions of a certain fourth order Euler equations
en
en
In this paper, using Laplace transform technique, we propose the generalized solutions of the fourth order Euler differential equations \[t^4y^{(4)}(t)+t^3y'''(t)+t^2y''(t)+ty'(t)+my(t)=0,\] where \(m\) is an integer and \(t\in\mathbb{R}\). We find types of solutions depend on the values of \(m\). Precisely, we have a distributional solution for \(m=-k^4-5k^3-9k^2-4k\) and a weak solution for \(m=-k^4+5k^3-9k^2+4k,\) where \(k\in\mathbb{N}.\)
4077
4084
Amphon
Liangprom
Department of Mathematics
Khon Kaen University
Thailand
amphonred@gmail.com
Kamsing
Nonlaopon
Department of Mathematics
Khon Kaen University
Thailand
nkamsi@kku.ac.th
Generalized solution
distributional solution
Euler equation
Dirac delta function.
Article.4.pdf
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]
On some common coupled fixed point results in rectangular \(b\)-metric spaces
On some common coupled fixed point results in rectangular \(b\)-metric spaces
en
en
In this paper, by using the \(w\)-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular \(b\)-metrics. Some new common coupled fixed point theorems are obtained. We also provide
illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.
4085
4098
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
mathgufeng@163.com
Rectangular b-metric space
coupled coincidence point
common coupled fixed point
w-compatible mapping pairs.
Article.5.pdf
[
[1]
M. Abbas, M. A. Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
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T. Abdeljawad, D. Türkoğlu , Locally convex valued rectangular metric spaces and the Kannan’s fixed point theorem, J. Comput. Anal. Appl., 14 (2012), 484-494
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M. Arshad, J. Ahmad, E. Karapınar , Some common fixed point results in rectangular metric spaces, Int. J. Anal., 2013 (2013), 1-7
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H. Aydi, A. Felhi, S. Sahmim, Common fixed points in rectangular b-metric spaces using (E.A) property, J. Adv. Math. Stud., 8 (2015), 159-169
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H.-S. Ding, M. Imdad, S. Radenović, J. Vujaković , On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab J. Math. Sci., 22 (2016), 151-164
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˙I. M. Erhan, E. Karapınar, T. Sekulić, Fixed points of (\(\psi,\phi\)) contractions on rectangular metric spaces , Fixed Point Theory Appl., 2012 (2012), 1-12
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R. George, S. Radenović, K. P. Reshma, S. Shukla, Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8 (2015), 1005-1013
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R. George, R. Rajagopalan, Common fixed point results for \(\psi-\phi\) contractions in rectangular metric spaces, Bull. Math. Anal. Appl., 5 (2013), 44-52
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H. Isık, D. Türkoğlu, Common fixed points for ( \(\psi,\alpha,\beta\))-weakly contractive mappings in generalized metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-6
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W. A. Kirk, N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., 2013 (2013), 1-9
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B. K. Lahiri, P. Das , Fixed point of a Ljubomir Ćirić’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen, 61 (2002), 589-594
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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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H. Lakzian, B. Samet, Fixed points for (\(\psi,\phi\))-weakly contractive mappings in generalized metric spaces, Appl. Math. Lett., 25 (2012), 902-906
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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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J. R. Roshan, V. Parvaneh, Z. Kadelburg, H. Zoran , New fixed point results in b-rectangular metric spaces, Nonlinear Anal. Model. Control, 21 (2016), 614-634
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B. Samet, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal. (Ruse), 3 (2009), 1265-1271
]
Weak convergence of an iterative algorithm for accretive operators
Weak convergence of an iterative algorithm for accretive operators
en
en
In this paper, an iterative algorithm investigated for \(m\)-accretive and inverse-strongly accretive operators. Also, a weak convergence theorem for the sum of two accretive operators is established in a real uniformly convex and \(q\)-uniformly
smooth Banach space.
4099
4108
Hengjun
Zhao
School of Science
Henan University of Engineering
China
Sun Young
Cho
Center for General Education
China Medical University
Taiwan
ooly61@hotmail.com
Accretive operator
zero point
projection
splitting method
weak convergence.
Article.6.pdf
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D. E. Alspach, A fixed point free nonexpansive map , Proc. Amer. Math. Soc., 82 (1981), 423-424
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##[4]
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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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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]
Relaxed inertial accelerated algorithms for solving split equality feasibility problem
Relaxed inertial accelerated algorithms for solving split equality feasibility problem
en
en
In this paper, we study the split equality feasibility problem and present two algorithms for solving the problem with special structure. We prove the weak convergence of these algorithms under mild conditions. Especially, the selection of stepsize is only dependent on the information of current iterative points, but independent from the prior knowledge of operator norms. These algorithms provide new ideas for solving the split equality feasibility problem. Numerical results demonstrate the feasibility and effectiveness of these algorithms.
4109
4121
Meixia
Li
School of Mathematics and Information Science
Weifang University
China
limeixia001@163.com
Xiping
Kao
College of Mathematics and Systems Science
Shandong University of Science and Technology
China
805357576@qq.com
Haitao
Che
School of Mathematics and Information Science
Weifang University
China
haitaoche@163.com
Split equality feasibility problem
relaxed inertial accelerated algorithm
weak convergence
subdifferential.
Article.7.pdf
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]
Second-order accurate numerical approximations for the fractional percolation equations
Second-order accurate numerical approximations for the fractional percolation equations
en
en
First, we examine a practical numerical method which based on the classical Crank-Nicholson (CN) method combined with Richardson extrapolation is used to solve a class of one-dimensional initial-boundary value fractional percolation equation (FPE) with variable coefficients on a finite domain. Secondly, we present ADI-CN method for the two-dimensional fractional percolation equation. Stability and convergence of these methods are proved. Using these methods, we can achieve second-order convergence in time and space. Finally, numerical examples are presented to verify the order of convergence.
4122
4136
Xiucao
Yin
Department of Mathematics
South China Agricultural University
P. R. China
tanzhen2856@163.cn
Lang
Li
Department of Mathematics
South China Agricultural University
P. R. China
lilang05422@163.com
Shaomei
Fang
Department of Mathematics
South China Agricultural University
P. R. China
dz90@scau.edu.cn
The fractional percolation equations
Crank-Nicholson method
ADI-CN method
stability
convergence
Richardson extrapolation.
Article.8.pdf
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S. Chen, F. Liu, V. Anh , A novel implicit finite difference method for the one-dimensional fractional percolation equation, Numer. Algorithms, 56 (2011), 517-535
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S. Chen, F. Liu, K. Burrage , Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media, Comput. Math. Appl., 68 (2014), 2133-2141
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S. Chen, F. Liu, I. Turner, V. Anh , An implicit numerical method for the two-dimensional fractional percolation equation, Appl. Math. Comput., 219 (2013), 4322-4331
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H. Chou, B. Lee, C. Chen , The transient infiltration process for seepage flow from cracks, Advances in Subsurface Flow and Transport: Eastern and Western Approaches III, (2006)
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B. Guo, Q. Xu, Z. Yin, Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions, Appl. Math. Mech., 37 (2016), 403-416
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B. Guo, Q. Xu, A. Zhu , A second-order finite difference method for two-dimensional fractional percolation equations, Commun. Comput. Phys., 19 (2016), 733-757
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M. S. Hashemi, E. Darvishi, D. Baleanu, A geometric approach for solving the density-dependent diffusion Nagumo equation, Adv. Difference Equ., 2016 (2016), 1-13
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H. M. Srivastava, D. Kumar, J. Singh, An efficient analytical technique for fractional model of vibration equation, Appl. Math. Model., 45 (2017), 192-204
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Y. Zhang, D. Baleanu, X.-J. Yang, New solutions of the transport equations in porous media within local fractional derivative, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 17 (2016), 230-236
]
Some identities of \(\lambda\)-Daehee polynomials
Some identities of \(\lambda\)-Daehee polynomials
en
en
In this paper, we give some identities of \(\lambda\)-Daehee polynomials and investigate a new and interesting identities of \(\lambda\)-Daehee polynomial arising from the symmetry properties of the \(p\)-adic invariant integral on \(\mathbb{Z}_p\).
4137
4142
Jeong Gon
Lee
Division of Mathematics and informational Statistics, Nanoscale Science and Technology Institute
Wonkwang University
Republic of Korea
jukolee@wku.ac.kr
Jongkyum
Kwon
Department of Mathematics Education and RINS
Gyeongsang National University
Republic of Korea
mathkjk26@gnu.ac.kr
Gwan-Woo
Jang
Department of Mathematics
Kwangwoon University
Republic of Korea
jgw5687@naver.com
Lee-Chae
Jang
Graduate school of Education
Konkuk University
Republic of Korea
lcjang@konkuk.ac.kr
\(\lambda\)-Daehee polynomials
\(p\)-adic invariant integral on \(\mathbb{Z}_p\).
Article.9.pdf
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[1]
S. Araci, O. Ozen, Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials, Adv. Difference Equ., 2015 (2015), 1-5
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Y.-K. Cho, T. Kim, T. Mansour, S.-H. Rim , Higher-order q-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 167-173
##[3]
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
##[4]
D. V. Dolgy, D. S. Kim, T. Kim, On Korobov polynomials of the first kind, (Russian) Mat. Sb., 208 (2017), 65-79
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D. V. Dolgy, D. S. Kim, T. Kim, T. Mansour, Barnes-type Daehee with \(\lambda\) -parameter and degenerate Euler mixed-type polynomials, J. Inequal. Appl., 2015 (2015), 1-13
##[6]
B. S. El-Desouky, A. Mustafa , New results on higher-order Daehee and Bernoulli numbers and polynomials , Adv. Difference Equ., 2016 (2016), 1-21
##[7]
T. Kim, Symmetry p-adic invariant integral on \(\mathbb{Z}_p\) for Bernoulli and Euler polynomials, J. Difference Equ. Appl., 14 (2008), 1267-1277
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T. Kim , Symmetry of power sum polynomials and multivariate fermionic p -adic invariant integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 93-96
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T. Kim, An identity of the symmetry for the Frobenius-Euler polynomials associated with the fermionic p-adic invariant q-integrals on \(\mathbb{Z}_p\), Rocky Mountain J. Math., 41 (2011), 239-247
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T. Kim, D. V. Dolgy, D. S. Kim, Some identities of q -Bernoulli polynomials under symmetry group \(S_3\), J. Nonlinear Convex Anal., 16 (2015), 1869-1880
##[11]
D. S. Kim, T. Kim, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196-208
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D. S. Kim, T. Kim, Some identities of Boole and Euler polynomials, Ars Combin., 118 (2015), 349-356
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D. S. Kim, T. Kim, Some identities of symmetry for Carlitz q -Bernoulli polynomials invariant under \(S_4\), Ars Combin., 123 (2015), 283-289
##[14]
D. S. Kim, T. Kim , Some identities of symmetry for q -Bernoulli polynomials under symmetric group of degree n, Ars Combin., 126 (2016), 435-441
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T. Kim, D. S. Kim, On \(\lambda\)-Bell polynomials associated with umbral calculus, Russ. J. Math. Phys., 24 (2017), 69-78
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D. S. Kim, T. Kim, S.-H. Lee,, Higher-order Daehee of the first kind and poly-Cauchy of the first kind mixed type polynomials, , J. Comput. Anal. Appl., 18 (2015), 699-714
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D. S. Kim, T. Kim, S.-H. Lee, J.-J. Seo, Identities of symmetry for higher-order q-Euler polynomials , Proc. Jangjeon Math. Soc., 17 (2014), 161-167
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D. S. Kim, N. Lee, J. Na, K. H. Park , Identities of symmetry for higher-order Euler polynomials in three variables (I), Adv. Stud. Contemp. Math., 22 (2012), 51-74
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D. S. Kim, N. Lee, J. Na, K. H. Park, Abundant symmetry for higher-order Bernoulli polynomials (I), Adv. Stud. Contemp. Math., 23 (2013), 461-482
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E.-M. 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
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H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q -Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math., 18 (2009), 41-48
##[22]
J. J. Seo, T. Kim, Some identities of symmetry for Daehee polynomials arising from p -adic invariant integral on \(\lambda\) , Proc. Jangjeon Math. Soc., 19 (2016), 285-292
##[23]
Y. Simsek, A. Yardimci , Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and p-adic integrals, Adv. Difference Equ., 2016 (2016), 1-14
]
Convergence analysis of a Halpern-like iterative algorithm in Hilbert spaces
Convergence analysis of a Halpern-like iterative algorithm in Hilbert spaces
en
en
In this paper, a Halpern-like iterative algorithm is investigated for finding a solution of a split feasibility problem and a solution to a nonexpansive operator equation. Strong convergence theorems are established in the framework of infinite dimensional Hilbert spaces.
4143
4149
Yunpeng
Zhang
College of Electric Power
North China University of Water Resources and Electric Power
China
zhangypliyl@yeah.net
Sun Young
Cho
Center for General Education
China Medical University
Taiwan
ooly61@hotmail.com
Convergence analysis
Hilbert space
monotone mapping
split feasibility problem.
Article.10.pdf
[
[1]
B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2005), 1-14
##[2]
B. A. Bin Dehaish, X. Qin, A. Latif, H. Bakodah , Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
##[3]
F. E. Browder , Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Natl. Acad. Sci. U.S.A., 53 (1965), 1272-1276
##[4]
C. Byrne , A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl., 20 (2004), 103-120
##[5]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[6]
Y. Censor, T. Elfving , A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[7]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Probl., 21 (2005), 2071-2084
##[8]
S. Y. Cho, B. A. Bin Dehaish, X. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
##[9]
S. Y. Cho, S. M. Kang, Approximation of common solutions of variational inequalities via strict pseudocontractions , Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 1607-1618
##[10]
S. Y. Cho, W. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 1-14
##[11]
N. Fang, Y. Gong , Viscosity iterative methods for split variational inclusion problems and fixed poit problems of a nonexpansive mappings, Commun. Optim. Theory, 2016 (2016), 1-15
##[12]
L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194 (1995), 114-125
##[13]
X. Qin, S. S. Chang, Y. J. Cho, Iterative methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal. Real World App., 11 (2010), 2963-2972
##[14]
X. 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
##[15]
X. Qin, J. C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[16]
W. Takahahsi , Weak and strong convergence theorems for families of nonlinear and nonself mappings in Hilbert spaces , J. Nonlinear Var. Anal., 1 (2017), 1-23
##[17]
J. Tang, S. S. Chang, Strong convergence theorem of two-step iterative algorithm for split feasibility problems, J. Inequal. Appl., 2014 (2014), 1-13
##[18]
J. Tang, S. S. Chang, J. Dong, Split equality fixed point problems for two quasi-asymptotically pseudocontractive mappings, J. Nonlinear Funct. Anal., 2017 (2017), 1-15
##[19]
H. Y. Zhou, Y.Wang, Adaptively relaxed algorithms for solving the split feasibility problem with a new step size, J. Inequal. Appl., 2014 (2014), 1-22
]
Some properties and mappings on weakly \(\nu \)-Lindelöf generalized topological spaces
Some properties and mappings on weakly \(\nu \)-Lindelöf generalized topological spaces
en
en
Our work aims to study weakly \(\nu \)-Lindelöf (briefly \(w\nu \)-Lindelöf) space in generalized topological spaces. Some characterizations of \(w\nu \)-Lindelöf subspaces and subsets are showed.
Furthermore, we shall show that the \(w\nu \)-Lindelöf generalized topological space is not a hereditary property. Finally, the effect of some mappings and decompositions of continuity are studied. The main result that we obtained on is the effect of almost \((\nu, \mu)\)-continuous function on \(w\nu \)-Lindelöf generalized topological space.
4150
4161
M.
Abuage
Institute for Mathematical Research
University Putra Malaysia
Malaysia
slaa.salem@yahoo.com
A.
Kılıçman
Department of Mathematics
University Putra Malaysia
Malaysia
akilic@upm.edu.my
\(\nu \)-Lindelöf
\(w\nu \)-Lindelöf
\(G\)-semiregular generalized topological space.
Article.11.pdf
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[1]
M. Abuage, A. Kılıçman, Some Properties and Decomposition on \(a\nu \)-Lindelöf generalized topological spaces, , (submitted), -
##[2]
M. Abuage, A. Kılıçman, M. S. Sarsak, Generalization of soft \(\nu \)-compact soft generalized topological spaces, arXiv, 2016 (2016), 1-10
##[3]
M. Abuage, A. Kılıçman, M. S. Sarsak, \(n\nu \)-Lindelöfness, Malay. J. Math. Sci., 11 (2017), 73-86
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A. Al-omari, T. Noiri, A unified theory of contra-(\(\nu,\lambda\))-continuous functions in generalized topological spaces, Acta Math. Hungar., 135 (2012), 31-41
##[5]
M. Arar , A note on spaces with a countable \(\nu \)-base, Acta Math. Hungar., 144 (2014), 494-498
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J. B. T. Ayawan, J. S. R. Canoy , Axioms of Countability in Generalized Topological Spaces, Int. Math. Forum, 8 (2013), 1523-1530
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Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), 53-66
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Á. Császár , Further remarks on the formula of \(\gamma\)-interior, Acta Math. Hungar., 113 (2006), 325-332
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]
Some applications with new admissibility contractions in \(b\)-metric spaces
Some applications with new admissibility contractions in \(b\)-metric spaces
en
en
The work presented in this paper extends the idea of \(\alpha-\beta\)-contractive mappings in the framework of \(b\)-metric spaces. Fixed points are investigated for such kind of mappings. An example is given to show the superiority of our results. As applications we discuss Ulam-Hyres stability, well-posedness
and limit shadowing of fixed point problem.
4162
4174
Ljiljana
Paunović
University of Pristina-Kosovska Mitrovica, Teacher Education School in Prizren-Leposavic
Serbia
ljiljana.paunovic76@gmail.com
Preeti
Kaushik
Department of Mathematics
DCRUST
India
preeti1785@gmail.com
Sanjay
Kumar
Department of Mathematics
DCRUST
India
sanjaymudgal2004@yahoo.com
\(\alpha-\beta(b)\)-admissible mappings
fixed point
\(b\)-metric space
stability.
Article.12.pdf
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M. F. Bota, E. Karapnar, O. Mlesnite, Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\)-contractive mapping in (b)-metric space, Abstr. Appl. Anal., 2013 (2013), 1-6
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G. S. Rad, S. Radenović, D. Dolićanin-Dekić, A shorter and simple approach to study fixed point results via b-simulation functions, Iran. J. Math. Sci. Inform., (Accepted), -
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]
Lie group method and fractional differential equations
Lie group method and fractional differential equations
en
en
In this paper, Lie group method is applied to investigate and solve
some classes of nonlinear fractional differential equations. In
addition, we use the obtained symmetries to induce exact solutions for the equations under consideration.
4175
4180
M. M.
Alshamrani
Department of Mathematics, Faculty of Science
Northern Border University
Saudi Arabia
malshomrani@hotmail.com
H. A.
Zedan
Department of Mathematics, Faculty of Science
Kafrelsheikh University
Egypt
hassanzedan2003@yahoo.com
M.
Abu-Nawas
Department of Mathematics, Faculty of Science
Northern Border University
Saudi Arabia
m.abunawas.math.nbu@gmail.com
Lie group method
nonlinear partial differential equations
symmetry analysis.
Article.13.pdf
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M. A. Abdelkawy, M. A. Zaky, A. H. Bhrawy, D. Baleanu , Numerical simulation of time variable fractional order mobile-immobile advection-dispersion model , Rom. Rep. Phys., 67 (2015), 773-791
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A. Agila, D. Baleanu, R. Eid, B. Irfanoglu , Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems, Rom. J. Phys., 61 (2016), 350-359
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W. F. Ames, R. L. Anderson, V. A. Dorodnitsyn, E. V. Ferapontov, R. K. Gazizov, N. H. Ibragimov, S. R. Svirshchevskiĭ, CRC handbook of Lie group analysis of differential equations, Vol. 1, Symmetries, exact solutions and conservation laws. CRC Press, Boca Raton, FL (1994)
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A. H. Bhrawy , A new spectral algorithm for time-space fractional partial differential equations with subdiffusion and superdiffusion, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci., 17 (2016), 39-47
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E. H. El Kinani, A. Ouhadan, Lie symmetry analysis of some time fractional partial differential equations, Int. J. Mod. Phys., 38 (2015), 1-8
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Q. Huang, R. Zhdanov , Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative , Phys. A, 409 (2014), 110-118
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D. Kumar, J. Singh, D. Baleanu, A fractional model of convective radial fins with temperature-dependent thermal conductivity, Rom. Rep. Phys., 69 (2017), 1-13
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K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York (1993)
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K. Nouri, S. Elahi-Mehr, L. Torkzadeh, Investigation of the behavior of the fractional Bagley-Torvik and Basset equations via numerical inverse Laplace transform, Rom. Rep. Phys., 68 (2016), 503-514
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K. B. Oldham, J. Spanier, The fractional calculus, Theory and applications of differentiation and integration to arbitrary order, With an annotated chronological bibliography by Bertram Ross, Mathematics in Science and Engineering, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1974)
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R. Sahadevan, T. Bakkyaraj , Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations , J. Math. Anal. Appl., 393 (2012), 341-347
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G.-W. Wang, X.-Q. Liu, Y.-Y. Zhang, Lie symmetry analysis to the time fractional generalized fifth-order KdV equation, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 2321-2326
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G.-W.Wang, T.-Z. Xu, Invariant analysis and explicit solutions of the time fractional nonlinear perturbed Burgers equation , Nonlinear Anal. Model. Control, 20 (2015), 570-584
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H. Zedan, M. M. Alshamrani, A novel class of solutions for the (2 + 1)-dimensional higher-order Broer-Kaup system, Comput. Math. Appl., 69 (2015), 67-80
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M. Zurigat, S. Momani, Z. Odibat, A. Alawneh , The homotopy analysis method for handling systems of fractional differential equations, Appl. Math. Model., 34 (2010), 24-35
]
Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays
Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays
en
en
Keeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results.
4181
4196
Jiangang
Zhang
School of Mathematics and Physics
Lanzhou Jiaotong University
China
zhangjg7715776@126.com
Jiarong
Lu
School of Mathematics and Physics
Lanzhou Jiaotong University
China
ljrong1203@126.com
Wenju
Du
School of Traffic and Transportation
Lanzhou Jiaotong University
China
duwenjuok@126.com
Yandong
Chu
School of Mathematics and Physics
Lanzhou Jiaotong University
China
cyd@mail.lzjtu.cn
Hongwei
Luo
School of Mathematics and Physics
Department of Information Engineering
Lanzhou Jiaotong University
Gansu Forestry Technological College
China
China
lhw1220@126.com
Tritrophic Hastings-Powell model
local stability
delays
Hopf bifurcation.
Article.14.pdf
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C. Califano, C. H. Moog , Accessibility of nonlinear time-delay systems, IEEE Trans. Automat. Control, 62 (2017), 1254-1268
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C. Çelik, Stability and Hopf bifurcation in a delayed ratio dependent Holling-Tanner type model, Appl. Math. Comput., 255 (2015), 228-237
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Y.-Y. Chen, J. Yu, C.-J. Sun , Stability and Hopf bifurcation analysis in a three-level food chain system with delay, Chaos Solitons Fractals, 31 (2007), 683-694
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K. P. Das, S. Chatterjee, J. Chattopadhyay, Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from Hastings–Powell model, Ecol. Complexity, 6 (2009), 363-374
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S. Gakkhar, A. Singh, Control of chaos due to additional predator in the Hastings-Powell food chain model, J. Math. Anal. Appl., 385 (2012), 423-438
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J. K. Hale, Functional differential equations, Applied Mathematical Sciences, Springer-Verlag, New York–Heidelberg (1971)
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Z.-J. Li, Z.-T. Chen, J. Fu, C.-Y. Sun, Direct adaptive controller for uncertain MIMO dynamic systems with time-varying delay and dead-zone inputs, Automatica J. IFAC, 63 (2016), 287-291
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A. E. Matouk, A. A. Elsadany, E. Ahmed, H. N. Agiza , Dynamical behavior of fractional-order Hastings-Powell food chain model and its discretization , Commun. Nonlinear Sci. Numer. Simul., 27 (2015), 153-167
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C.-R. Tian, L. Zhang, Hopf bifurcation analysis in a diffusive food-chain model with time delay, Comput. Math. Appl., 66 (2013), 2139-2153
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Z.-X. Yu, Y. Dong, S.-G. Li, F.-F. Li, Adaptive tracking control for switched strict-feedback nonlinear systems with timevarying delays and asymmetric saturation actuators, Neurocomputing, 238 (2017), 245-254
##[16]
L.-Y. Zhang, Hopf bifurcation analysis in a Monod-Haldane predator-prey model with delays and diffusion, Appl. Math. Model., 39 (2015), 1369-1382
##[17]
Y.-M. Zhang, J.-D. Cao, W.-Y. Xu , Stability and Hopf bifurcation of a Goodwin model with four different delays, Neurocomputing, 165 (2015), 144-151
##[18]
Y.-J. Zhang, Y.-S. Ou, X.-Y. Wu, Y.-M. Zhou, Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays, Nonlinear Anal. Hybrid Syst., 24 (2017), 13-27
##[19]
Z.-X. Zhong, J.-Y. Yu, Y.-D. He, T. Hayat, F. Alsaadi, Fuzzy-model-based decentralized dynamic-output-feedback \(H^\infty\) control for large-scale nonlinear systems with time-varying delays, Neurocomputing, 173 (2016), 1054-1065
]
Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications
Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications
en
en
The aim of this paper is to define
generalized \((\alpha-\eta)-\Theta\) contraction and to extend the results of Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., \(\bf{2014}\) (2014), 8 pages] by applying a simple condition on the function \(\Theta\). We also deduce certain fixed and
periodic point results for orbitally continuous generalized \(\Theta \)-contractions and certain fixed point results for integral inequalities are derived. Finally, we provide an example to show the significance of the
investigation of this paper.
4197
4208
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Abdullah Eqal
Al-Mazrooei
Department of Mathematics
University of Jeddah
Saudi Arabia
aealmazrooei@uj.edu.sa
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jkhan@uj.edu.sa;jamshaid_jasim@yahoo.com
Fixed point
complete metric space
\(\alpha\)-admissible mapping.
Article.15.pdf
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[1]
R. P. Agarwal, N. Hussain, M. A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstr. Appl. Anal., 2012 (2012), 1-15
##[2]
J. Ahmad, A. E. Al-Mazrooei, Y. J. Cho, Y.-O. Yang , Fixed point results for generalized \(\Theta\)-contractions, J. Nonlinear Sci. Appl., 10 (2017), 2350-2358
##[3]
J. Ahmad, A. Al-Rawashdeh, A. Azam, Fixed point results for \(\{\alpha,\xi\}\)-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 1-10
##[4]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
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J. Ahmad, N. Hussain, A. Azam, M. Arshad , Common fixed point results in complex valued metric space with applications to system of integral equations , J. Nonlinear Convex Anal., 29 (2015), 855-871
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A. Al-Rawashdeh, J. Ahmad , Common fixed point theorems for JS-contractions, Bull. Math. Anal. Appl., 8 (2016), 12-22
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Z. Aslam, J. Ahmad, N. Sultana, New common fixed point theorems for cyclic compatible contractions, J. Math. Anal., 8 (2017), 1-12
##[8]
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, General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces , Carpathian J. Math., 24 (2008), 10-19
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M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79
##[12]
N. Hussain, J. Ahmad, A. Azam, Generalized fixed point theorems for multi-valued \(\alpha-\psi\)-contractive mappings, J. Inequal. Appl., 2014 (2014), 1-15
##[13]
N. Hussain, J. Ahmad, L. Ćirić, A. Azam , Coincidence point theorems for generalized contractions with application to integral equations, Fixed Point Theory Appl., 2015 (2015), 1-13
##[14]
N. Hussain, S. Al-Mezel, P. Salimi , Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl. Anal., 2013 (2013), 1-11
##[15]
N. Hussain, M. A. Kutbi, S. Khaleghizadeh, P. Salimi, Discussions on recent results for \(\alpha-\psi\)-contractive mappings, Abstr. Appl. Anal., 2014 (2014), 1-13
##[16]
N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications , Abstr. Appl. Anal., 2014 (2014), 1-11
##[17]
N. Hussain, V. Parvaneh, B. Samet, C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-17
##[18]
N. Hussain, M. A. Taoudi , Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl., 2013 (2013), 1-16
##[19]
M. Jleli, B. Samet , A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[20]
P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 1-19
##[21]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\) -contractive type mappings , Nonlinear Anal., 75 (2012), 2154-2165
]
Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model
Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model
en
en
The global well-posedness analysis for the three dimensional dynamic Cahn-Hilliard-Stokes (CHS) model is provided in this paper. In this model, the velocity vector is determined by the phase variable by both the Darcy law and the Stokes equation. Based on the analysis of weak solutions to the CHS equation by the standard Galerkin method, we present a global in time strong solution for the CHS model. Moreover, the existence and the uniqueness of the strong solution are also proven.
4209
4221
Kelong
Cheng
School of Science
Southwest University of Science and Technology
China
zhengkelong@swust.edu.cn
Wenqiang
Feng
Department of Mathematics
University of Tennessee
USA
wfeng1@vols.utk.edu
Cahn-Hilliard-Stokes model
Sobolev embedding
Galerkin procedure
Hemlholtz projection.
Article.16.pdf
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[1]
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Optimal harvesting policy of a stochastic delay predator-prey model with Lévy jumps
Optimal harvesting policy of a stochastic delay predator-prey model with Lévy jumps
en
en
This paper considers the optimal harvesting of a stochastic delay predator-prey model with Lévy jumps. The traditional optimal harvesting problem of this type of model is difficult because it is difficult to get the explicit solutions of the model or to solve the corresponding delay Fokker-Planck equation of the model. In this paper, we use an ergodic method to study this problem, and establish the sufficient and necessary conditions for the existence of an optimal harvesting strategy of the model. In addition, we gain the explicit forms of the optimal harvesting effort and the maximum of the cost function. One can see that the ergodic method used in this paper can avoid solving both the model and the corresponding delay Fokker-Planck equation.
4222
4230
Meiling
Deng
School of Mathematical Science
Huaiyin Normal University
P. R. China
hnudengmeiling@163.com
Predator-prey system
random perturbations
delay
optimal harvesting.
Article.17.pdf
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[1]
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New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws
New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws
en
en
The mathematical equation that describes how the quantum state of a quantum system changes during time was considered within the framework of fractional differentiation with three
different derivatives in Riemann-Liouville sense. The fractional derivatives used in this work are constructed based on power, exponential decay, and Mittag-Leffler law. A new numerical scheme for fractional derivative in Riemann-Liouville sense is presented and used to solve numerically the Schrödinger equation. The stability analysis of each model is presented in
detail.
4231
4243
Badr Saad T.
Alkahtani
Department of mathematics, colle of science
King Saud University
Saudi Arabia
balqahtani1@ksu.edu.sa
Ilknur
Koca
Department of Mathematics, Faculty of Sciences
Mehmet Akif Ersoy University
Turkey
ikoca@mehmetakif.edu.tr
Abdon
Atangana
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
abdonatangana@yahoo.fr
Power law
exponential decay law
Mittag-Leffler law
numerical scheme
Schrödinger equation.
Article.18.pdf
[
[1]
O. J. J. Algahtani , Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model , Chaos Solitons Fractals, 89 (2016), 552-559
##[2]
T. B. S. Alkahtani, Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89 (2016), 547-551
##[3]
A. Atangana , On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation , Appl. Math. Comput., 273 (2016), 948-956
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A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model , Therm. Sci., 20 (2016), 763-769
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A. Atangana, J. F. Gomez-Aquilar, Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann- Liouville to Atangana-Baleanu, Appl. Numer. Math., (2016), -
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A. Atangana, I. Koca , Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order , Chaos Solitons Fractals, 89 (2016), 447-454
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H. Bulut, F. B. M. Belgacem, H. M. Baskonus , Some new analytical solutions for the nonlinear Time-Fractional KdVBurgers- Kuramoto equation, Adv. Math. Stat. Sci., 2 (2015), 118-129
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J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel , Progr. Fract. Differ. Appl., 1 (2015), 87-92
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S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives , Theory and applications, Edited and with a foreword by S. M. Nikol'skiĭ, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
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X.-J. Yang , Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems, Therm. Sci., 21 (2016), 1161-1171
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X.-J. Yang, J. A. Tenreiro Machado, J. Hristov , Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow , Nonlinear Dynam., 84 (2016), 3-7
##[18]
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]
The extended Mittag-Leffler function via fractional calculus
The extended Mittag-Leffler function via fractional calculus
en
en
In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function:
\[
E_{\alpha,\beta}^{\gamma;q, c}(z)=\sum\limits_{n=0}^{\infty}\frac{B_p(\gamma+nq, c-\gamma)(c)_{nq}}{B(\gamma, c-\gamma)\Gamma(\alpha n+\beta)}\frac{z^n}{n!},~~~ (z,\beta, \gamma\in\mathbb{C}),
\]
as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels.
4244
4253
Gauhar
Rahman
Department of Mathematics
International Islamic University
Pakistan
gauhar55uom@gmail.com
Dumitru
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@cankaya.edu.tr
Maysaa Al
Qurashi
Department of Mathematics, College of Science
King Saud University
Saudia Arabia
maysaa@ksu.edu.sa
Sunil Dutt
Purohit
Department of HEAS (Mathematics)
Rajasthan Technical University
India
sunil a purohit@yahoo.com
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
Fractional integration
differential operator
Mittag-Leffler function
Lebesgue measurable function
extended Mittag-Leffler function.
Article.19.pdf
[
[1]
A. Agila, D. Baleanu, R. Eid, B. Irfanoglu , Applications of the extended fractional Euler-Lagrange equations model to freely oscillating dynamical systems , Rom. Journ. Phys., 61 (2016), 350-359
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A. Atangana, Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus, Eur. Phys. J. Plus, 2016 (2016), 1-13
##[3]
A. Atangana, D. Baleanu, New fractional derivatives with non-Local and non-singular kernel: theory and aplication to heat transfer model , Thermal Sci., 2016 (2016), 1-8
##[4]
A. Atangana, D. Baleanu, A. Alsaedi , Analysis of time-fractional Hunter-Saxton equation: a model of neumatic liquid crystal, Open Phys., 14 (2016), 145-149
##[5]
A. Atangana, C. Ünlü , New groundwater flow equation with its exact solution , Scientia Iranica, 23 (2016), 1837-1843
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D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo , Fractional Calculus Models and Numerical Methods, World Scientific, Singapore (2012)
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D. Baleanu, D. Kumar, S. D. Purohit, Generalized fractional integrals of product of two H-functions and a general class of polynomials, Int. J. Comput. Math., 93 (2016), 1320-1329
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D. Baleanu, S. D. Purohit, Chebyshev type integral inequalities involving the fractional hypergeometric operators, Abstr. Appl. Anal., 2014 (2014), 1-10
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D. Baleanu, S. D. Purohit, J. C. Prajapati , Integral inequalities involving generalized Erdelyi-Kober fractional integral operators, Open Math., 14 (2016), 89-99
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J. Choi, S. D. Purohit, A Grüss type integral inequality associated with gauss hypergeometric function fractional integral operator, Commun. Korean Math. Soc., 30 (2015), 81-92
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J. F. Gómez-Aguilar, A. Atangana, Fractional Hunter-Saxton equation involving partial operators with bi-order in Riemann-Liouville and Liouville-Caputo sense, Eur. Phys. J. Plus, 2017 (2017), 1-15
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J. F. Gómez-Aguilar, A. Atangana, New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications, Eur. Phys. J. Plus, 2017 (2017), 1-21
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R. Gorenflo, A. A. Kilbas, S. V. Rogosin, On the generalized Mittag-Leffler type functions , Integral Transform. Spec. Funct., 7 (1998), 215-224
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S. D. Purohit, R. K. Raina , Chebyshev type inequalities for the Saigo fractional integrals and their q-analogues, J. Math. Inequal., 7 (2013), 239-249
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S. D. Purohit, R. K. Raina, Certain fractional integral inequalities involving the Gauss hypergeometric function, Rev. Téc. Ing. Univ. Zulia, 37 (2014), 167-175
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]
Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings
Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings
en
en
In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem.
The results obtained in this paper generalize and improve the recent ones announced by many others.
4254
4268
Yaqin
Wang
Department of Mathematics
Shaoxing University
China
wangyaqin0579@126.com
Xiaoli
Fang
Department of Mathematics
Shaoxing University
China
fxl0418@126.com
Multiple-set split equality common fixed-point problem
demicontractive mapping
strong convergence.
Article.20.pdf
[
[1]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
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Y. Censor, T. Elfving, A multiprojection algorithm using Bergman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[3]
S. S. Chang, L. Wang, Y. Zhao, On a class of split equality fixed point problems in Hilbert spaces, J. Nonlinear Var. Anal., 1 (2017), 201-212
##[4]
C. E. Chidume, P. Ndambomve, A. N. Bello, The split equality fixed point problem for demi-contractive mappings, J. Nonlinear Anal. Optimiz., 6 (2015), 61-69
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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
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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. Zhao, S. Wang, Viscosity approximation methods for the split equality common fixed point problem of quasi-nonexpansive operators, Acta Math. Sci. Ser. B Engl. Ed., 36 (2016), 1474-1486
]
Essential norm of a product-type operator from Bergman space to weighted-type space
Essential norm of a product-type operator from Bergman space to weighted-type space
en
en
In this paper, we discuss the boundedness of a product-type operator
introduced by Stević, which acting from Bergman space to the
weighted-type spaces or the little weighted-type spaces in the unit
ball, and characterize the the essential norm of the product-type
operator. From which the sufficient and necessary condition of
compactness of this type operator follows immediately.
4269
4274
Ya-Song
Chen
Department of Mathematics
Tianjin Polytechnic University
P. R. China
yasongchen@126.com
Zhong-Shan
Fang
Department of Mathematics
Tianjin Polytechnic University
P. R. China
fangzhongshan@aliyun.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics and Intelligent Healthcare, 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
Product-type operator
Bergman space
weighted-type space
unit ball.
Article.21.pdf
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S. Stević, On a product-type operator from Bloch spaces to weighted-type spaces on the unit ball , Appl. Math. Comput., 217 (2011), 5930-5935
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Z.-H. Zhou, Y. Liu, The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications, J. Inequal. Appl., 2006 (2006), 1-22
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]
A version of the Stone-Weierstrass theorem in fuzzy analysis
A version of the Stone-Weierstrass theorem in fuzzy analysis
en
en
Let \(C(K,\mathbb{E}^1)\) be the space of continuous functions defined between a compact Hausdorff space \(K\) and the space of fuzzy numbers \(\mathbb{E}^1\) endowed with the supremum metric.
We provide a set of sufficient conditions on a subspace of \(C(K,\mathbb{E}^1)\) in order that it be dense. We also obtain a similar result for interpolating families of \(C(K,\mathbb{E}^1)\).
As a corollary of the above results we prove that certain fuzzy-number-valued neural networks can approximate any continuous fuzzy-number-valued function defined on a compact subspace of \(\mathbb{R}^n\).
4275
4283
Juan J.
Font
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
font@uji.es
Delia
Sanchis
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
dsanchis@uji.es
Manuel
Sanchis
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
sanchis@uji.es
Stone-Weierstrass theorem
fuzzy numbers
fuzzy-number-valued continuous functions.
Article.22.pdf
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]
Generalized convolution properties based on the modified Mittag-Leffler function
Generalized convolution properties based on the modified Mittag-Leffler function
en
en
Studies of convolution play an important role in Geometric Function
Theory (GFT). Such studies attracted a large number of researchers in recent years. By
making use of the Hadamard product (or convolution), several new and interesting subclasses
of analytic and univalent functions have been introduced and investigated in the direction of well-known
concepts such as the subordination and superordination inequalities,
integral mean and partial sums, and so on. In this article, we apply the
Hadamard product (or convolution) by utilizing some special
functions. Our contribution in this paper includes defining a new linear operator in the
form of the generalized Mittag-Leffler function in terms of the
extensively-investigated Fox-Wright \(\:_p\Psi_q\)-function in the right-half of the open unit disk where where \(\Re(z)>0.\) We then show that the new linear convolution operator is bounded in some spaces.
In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright \(\:_p\Psi_q\)-notation is used in our results.
4284
4294
H. M.
Srivastava
Department of Mathematics and Statistics
Center for General Education (Department of Science and Technology)
University of Victoria
China Medical University
Canada
Republic of China
harimsri@math.uvic.ca
Adem
Kılıçman
Department of Mathematics
Universiti Putra Malaysia
Malaysia
akilic@upm.edu.my
Zainab E.
Abdulnaby
Department of Mathematics
Department of Mathematics, College of Science
Universiti Putra Malaysia
Al-Mustansiriyah University
Malaysia
Iraq
esazainab@yahoo.com
Rabha W.
Ibrahim
Faculty of Computer Science and Information Technology
University of Malaya
Malaysia
rabhaibrahim@yahoo.com
Fractional calculus
analytic functions
fractional calculus operator
univalent functions
convex functions
Mittag-Leffler function
Fox-Wright \(\:_p\Psi_q\)-function
weighted \(\mu\)-Bloch space
weighted-log Bloch space.
Article.23.pdf
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Z. E. Abdulnaby, R. W. Ibrahim, A. Kılıçman, Some properties for integro-differential operator defined by a fractional formal , Springer Plus., 5 (2016), 1-9
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Z. E. Abdulnaby, H. M. Srivastava, A. Kılıçman, R. W. Ibrahim, A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain, Filomat, 31 (2017), 2837-2849
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R. Gorenflo, A. A. Kilbas, F. Mainardi, V. R. Sergei , Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin (2014)
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H. J. Haubold, A. M. Mathai, R. K. Saxena , Mittag-Leffler functions and their applications, J. Appl. Math., 2011 (2011), 1-51
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P. Humbert , Quelques résultat relatifs à la fonction de Mittag-Leffler, C. R. Acad. Sci. Paris, 236 (1953), 1467-1468
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A. A. Kilbas, M. Saigo, R. K. Saxena , Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transforms Spec. Funct., 15 (2004), 31-49
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo , Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
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A. Kılıçman, R. W. Ibrahim, Z. E. Abdulnaby, On a generalized fractional integral operator in a complex domain, Appl. Math. Inf. Sci., 10 (2016), 1053-1059
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V. S. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. appl. Math., 118 (2000), 241-259
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Y. Li, Y. Q. Chen, I. Podlubny, Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica J. IFAC, 45 (2009), 1965-1969
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J. Paneva-Konovska , Series in Mittag-Leffler functions: inequalities and convergent theorems, Fract. Calc. Appl. Anal., 13 (2010), 403-414
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M. Sharma , Fractional integration and fractional differentiation of the M-series, Fract. Calc. Appl. Anal., 11 (2008), 187-191
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K. Sharma, Application of fractional calculus operators to related areas, Gen. Math. Notes., 7 (2011), 33-40
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M. Sharma, R. Jain, A note on a generalized M-series as a special function of fractional calculus , Fract. Calc. Appl. Anal., 12 (2009), 449-452
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H. M. Srivastava , On an extension of the Mittag-Leffler function, Yokohama Math. J., 16 (1968), 77-88
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H. M. Srivastava , A new family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions with application, Appl. Math. Inform. Sci., 8 (2014), 1485-1500
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H. M. Srivastava, R. K. Saxena, Operators of fractional integration and their applications, Appl. Math. Comput., 118 (2001), 1-52
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H. M. Srivastava, R. K. Saxena, T. K. Pogány, R. Saxena, Integral and computational representations of the extended Hurwitz-Lerch zeta function , Integral Transforms Spec. Funct., 22 (2011), 487-506
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H. M. Srivastava, R. K. Saxena, C. Ram , A unified presentation of the Gamma-type functions occurring in diffraction theory and associated probability distributions, Appl. Math. comput., 162 (2005), 931-947
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H. M. Srivastava, Z . Tomovski , Fractional calculus with an integral operator containing a generalized MittagLeffler function in the kernel, J. Appl. Math. Comput., 211 (2009), 198-210
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Z . Tomovski, R. Hilfer, H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms and Spec. Funct., 21 (2010), 797-814
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A. Wiman , Über den Fundamentalsatz in der Teorie der Funktionen \(E_\alpha(x)\), Acta. Math., 29 (1905), 191-201
]
Boundedness of high order commutators of Marcinkiewicz integrals associated with Schrödinger operators
Boundedness of high order commutators of Marcinkiewicz integrals associated with Schrödinger operators
en
en
Suppose \(L=-\Delta+V\) is a Schrödinger operator on \(\mathbb{R}^n\), where \(n\geq 3\)
and the nonnegative potential \(V\) belongs to reverse Hölder class \(RH_{n}.\) Let \(b\) belong to a new Campanato space \(\Lambda_\beta^\theta(\rho),\) and let \(\mu_j^L\) be the Marcinkiewicz integrals associated with \(L.\) In this paper, we establish the boundedness of the \(m\)-order commutators \([b^m, \mu_j^L]\) from \(L^p(\mathbb{R}^n)\) to \(L^q(\mathbb{R}^n),\) where
\(1/q=1/p-m\beta/n\) and \(1<p<n/(m\beta).\) As an application, we obtain the boundedness of \([b^m, \mu_j^L]\) on the generalized Morrey spaces
related to certain nonnegative potentials.
4295
4306
Hui
Wang
Teachers College
Nanyang Institute of Technology
P. R. China
wanghui1639@126.com
Bijun
Ren
Department of Information Engineering
Henan Institute of Finance and Banking
P. R. China
renbijun1959@163.com
Schrödinger operator
Marcinkiewicz integral
commutator
Campanato space
Morrey space.
Article.24.pdf
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[1]
B. Bongioanni, E. Harboure, O. Salinas, Commutators of Riesz transforms related to Schrödinger operators, J. Fourier Anal. Appl., 17 (2011), 115-134
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D. Chen, F. Jin, The boundedness of Marcinkiewicz integrals associated with Schrödinger operator on Morrey spaces, J. Funct. Spaces, 2014 (2014), 1-11
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D. Chen, D. Zou, The boundedness of Marcinkiewicz integral associated with Schrödinger operator and its commutator, J. Funct. Spaces, 2014 (2014), 1-10
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J. Dziubański, J. Zienkiewicz , Hardy space \(H^1\) associated to Schrödinger operator with potential satisfying reverse Hölder inequality , Rev. Mat. Iberoamericana, 15 (1999), 279-296
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W. Gao, L. Tang , Boundedness for Marcinkiewicz integrals associated with Schrödinger operators, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 193-203
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Y. Liu, J. Sheng, Some estimates for commutators of Riesz transforms associated with Schrödinger operators, J. Math. Anal. Appl., 419 (2014), 298-328
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B. Ren, H. Wang, Boundedness of higher order Riesz transforms associated with Schrödinger type operator on generalized Morrey spaces, J. Nonlinear Sci. Appl., 10 (2017), 2757-2766
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Z. Shen, \(L^p\) estimates for Schrödinger operators with certain potentials, Ann. Inst. Fourier, 45 (1995), 513-546
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L. Tang, J. F. Dong, Boundedness for some Schrödinger type operator on Morrey spaces related to certain nonnegative potentials, J. Math. Anal. Appl., 355 (2009), 101-109
]
A coincidence-point problem of Perov type on rectangular cone metric spaces
A coincidence-point problem of Perov type on rectangular cone metric spaces
en
en
We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using \(\alpha\)-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.
4307
4317
Fairouz
Tchier
Mathematics Department College of Science (Malaz)
King Saud University
King Saudi Arabia
ftchier@ksu.edu.sa
Calogero
Vetro
Department of Mathematics and Computer Science
University of Palermo
Italy
calogero.vetro@unipa.it
Francesca
Vetro
Department of Energy, Information Engineering and Mathematical Models (DEIM)
University of Palermo
Italy
francesca.vetro@unipa.it
Rectangular cone metric space
spectral radius
solid cone
\(g-\)contraction of Perov type
\(\alpha\)-admissible mapping
\(\alpha-g-\)contraction of Perov type.
Article.25.pdf
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[1]
M. Abbas, V. Rakočević, A. Iqbal , Coincidence and common fixed points of Perov type generalized Ćirić-contraction mappings, Mediterr. J. Math., 13 (2016), 3537-3555
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M. Abbas, V. Rakočević, A. Iqbal , Fixed points of Perov type contractive mappings on the set endowed with a graphic structure, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM, (2017), 1-20
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J. Ahmad, M. Arshad, C. Vetro, On a theorem of Khan in a generalized metric space, Int. J. Anal., 2013 (2013), 1-6
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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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A. Azam, M. Arshad, I. Beg, Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math., 3 (2009), 236-241
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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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A. Branciari , A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37
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M. Cvetković, V. Rakočević, Common fixed point results for mappings of Perov type, Math. Nachr., 288 (2015), 1873-1890
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C. Di Bari, P. Vetro , Common fixed points in generalized metric spaces, Appl. Math. Comput., 218 (2012), 7322-7325
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Z. Kadelburg, S. Radenović, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci. (Springer), 8 (2014), 1-8
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Z. Kadelburg, S. Radenović, On generalized metric spaces: a survey , TWMS J. Pure Appl. Math., 5 (2014), 3-13
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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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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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S. K. Malhotra, S. Shukla, R. Sen, Some fixed point theorems for ordered Reich type contractions in cone rectangular metric spaces,, Acta Math. Univ. Comenian. (N.S.), 82 (2013), 165-175
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B. Samet , Discussion on ”A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces” by A. Branciari [ MR1771669], Publ. Math. Debrecen, 76 (2010), 493-494
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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
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S. Shukla, Reich type contractions on cone rectangular metric spaces endowed with a graph, Theory Appl. Math. Comput. Sci., 4 (2014), 14-25
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S. Shukla, S. Balasubramanian, M. Pavlović , A generalized Banach fixed point theorem, Bull. Malays. Math. Sci. Soc., 39 (2016), 1529-1539
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P. Vetro , Common fixed points in cone metric spaces , Rend. Circ. Mat. Palermo, 56 (2007), 464-468
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S.-Y. Xu, Ć . Dolićanin, S. Radenović, Some remarks on results of Perov type, J. Adv. Math. Stud., 9 (2016), 361-369
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P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Fourth International Conference on Function Spaces, Zielona Góra, (1995), Collect. Math., 48 (1997), 825-859
]
Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces
Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces
en
en
In this paper, we generalize the concept of \(\alpha\)-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms in Banach spaces. We establish some metric characterizations of \(\alpha\)-well-posedness and prove some equivalence results of strong \(\alpha\)-well-posedness (resp., in the generalized sense) between a system of time-dependent hemivariational inequalities and its derived system of inclusion problems.
4318
4336
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics and Intelligent Healthcare, 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
Jen-Chih
Yao
Center for General Education
China Medical University
Taiwan
yaojc@mail.cmu.edu.tw
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
China
yaoyonghong@aliyun.com
System of time-dependent hemivariational inequalities
\(\alpha\)-well-posedness
monotonicity
Clarke’s generalized gradient
regularity.
Article.26.pdf
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[1]
S. Carl, V. K. Le, D. Motreanu, Nonsmooth variational problems and their inequalities , Comparison principles and applications, Springer Monographs in Mathematics, Springer, New York (2007)
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L.-C. Ceng, H. Gupta, C.-F. Wen , Well-posedness by perturbations of variational-hemivariational inequalities with perturbations, Filomat, 26 (2012), 881-895
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L.-C. Ceng, Y. C. Lin, Metric characterizations of \(\alpha\)-well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces, J. Appl. Math., 2012 (2012), 1-22
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L.-C. Ceng, C.-F. Wen, Well-posedness by perturbations of generalized mixed variational inequalities in Banach spaces, J. Appl. Math., 2012 (2012), 1-38
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L.-C. Ceng, N.-C. Wong, J.-C. Yao, Well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations, J. Appl. Math., 2012 (2012), 1-21
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L. C. Ceng, J. C. Yao , Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems, Nonlinear Anal., 69 (2008), 4585-4603
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J.-W. Chen, Y. J. Cho, X.-Q. Ou, Levitin-Polyak well-posedness for set-valued optimization problems with constraints, Filomat, 28 (2014), 1345-1352
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A general iterative algorithm for vector equilibrium problem
A general iterative algorithm for vector equilibrium problem
en
en
In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied.
Firstly, an auxiliary problem for SVEP is introduced
and the relationships between the auxiliary problem and SVEP are discussed.
Then, based on the auxiliary problem, a general iterative algorithm for SVEP is proposed.
Moreover, analysis of convergence of this general iterative algorithm is investigated
under suitable conditions of cone-continuity and cone-convexity.
The main results obtained in this paper extend and develop the corresponding ones
of [A. N. Iusem, W. Sosa, Optimization, \(\bf 52\) (2003), 301--316], [S.-H. Wang, Q.-Y. Li,
Optimization, \(\bf 64\) (2015), 2049--2063], and [B. Cheng, S.-Y. Liu,
J. Lanzhou Univ. Nat. Sci., \(\bf 45\) (2009), 105--109].
4337
4351
Jin-xia
Huang
Department of Mathematics
Nanchang University
China
1335707969@qq.com
San-hua
Wang
Department of Mathematics
Post-doctor Station of Management Science and Engineering
Nanchang University
Nanchang University
China
China
wsh_ 315@163.com
Jia-yu
Mao
Department of Mathematics
Nanchang University
China
mjy_ 5965@163.com
Vector equilibrium problem
auxiliary problem
iterative algorithm
metric projection
cone-continuity.
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]
Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time scales
Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time scales
en
en
We study the existence of nonoscillatory solutions to a class of
third-order neutral functional dynamic equations on time scales. The
integral convergence and divergence of the reciprocal of the
coefficients in the equations are different. Two examples are given
to demonstrate the results.
4352
4363
Yang-Cong
Qiu
School of Humanities and Social Science
Shunde Polytechnic
P. R. China
q840410@qq.com
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
zadababo@yahoo.com
Shuhong
Tang
School of Information and Control Engineering
Weifang University
P. R. China
wfxytang@163.com
Tongxing
Li
School of Information Science and Engineering
School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China
Linyi University
P. R. China
litongx2007@163.com
Nonoscillatory solution
neutral dynamic equation
third-order
time scale.
Article.28.pdf
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]
The threshold of stochastic chemostat model with Monod-Haldane response function
The threshold of stochastic chemostat model with Monod-Haldane response function
en
en
This paper deals with problem of a stochastic chemostat model with Monod-Haldane response function. Firstly, we confirm the truth of the existence and uniqueness of the positive solution to the system. Then, we show the condition for the microorganism to be extinct. Moreover, we investigate there is a stationary distribution of this stochastic system and finally, we derive the expression for its invariant density.
4364
4371
Zhongwei
Cao
Department of Applied Mathematics
Jilin University of Finance and Economics
P. R. China
Caozw963@sina.com
Liya
Liu
College of Science
China University of Petroleum
P. R. China
liuliya_1993@hotmail.com
Stochastic chemostat model
threshold
extinction
persistence
stationary distribution.
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]
General \(L_p\)-mixed width-integral of convex bodies and related inequalities
General \(L_p\)-mixed width-integral of convex bodies and related inequalities
en
en
The conception of general \(L_p\)-mixed width-integral of convex bodies is introduced and related isoperimetric type inequality, Aleksandrov-Fenchel type inequality and a cyclic inequality are established. Further, the extremum values for the general \(L_p\)-mixed width-integral are obtained.
4372
4380
Yanping
Zhou
Department of Mathematics
Shanghai University
China
zhouyp@i.shu.edu.cn
general mixed width-integral
mixed width-integral
General \(L_p\)-mixed width-integral
convex body.
Article.30.pdf
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W. Weidong, W. Xiaoyan, Shephard type problems for general \(L_p\)-projection bodies, Taiwanese J. Math., 16 (2012), 1749-1762
]
Multiple periodic solutions for two classes of nonlinear difference systems involving classical \((\phi_1,\phi_2)\)-Laplacian
Multiple periodic solutions for two classes of nonlinear difference systems involving classical \((\phi_1,\phi_2)\)-Laplacian
en
en
In this paper, we investigate the
existence of multiple periodic solutions for two classes of nonlinear difference systems involving
\((\phi_1,\phi_2)\)-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we establish an existence theorem of three periodic solutions for
the first nonlinear difference system with \((\phi_1,\phi_2)\)-Laplacian and two parameters. Moreover, for the second nonlinear difference
system with \((\phi_1,\phi_2)\)-Laplacian, by using the Clark's Theorem, we obtain a
multiplicity result of periodic solutions under a symmetric
condition. Finally, two examples are given to verify
our theorems.
4381
4397
Xingyong
Zhang
Department of Mathematics, Faculty of Science
Kunming University of Science and Technology
P. R. China
zhangxingyong1@163.com
Liben
Wang
Department of Mathematics, Faculty of Science
Kunming University of Science and Technology
P. R. China
Difference systems
periodic solutions
multiplicity
variational approach.
Article.31.pdf
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[1]
G. Bonanno, P. Candito, Nonlinear difference equations investigated via critical point methods, Nonlinear Anal., 70 (2009), 3180-3186
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P. Candito, N. Giovannelli, Multiple solutions for a discrete boundary value problem involving the p-Laplacian, Comput. Math. Appl., 56 (2008), 959-964
##[3]
H.-Y. Deng, X.-Y. Zhang, H. Fang, Existence of periodic solutions for a class of discrete systems with classical or bounded \((\phi_1,\phi_2)\)-Laplacian, J. Nonlinear Sci. Appl., 10 (2017), 535-559
##[4]
Z.-M. Guo, J.-S. Yu, Existence of periodic and subharmonic solutions for second-order superlinear difference equations, Sci. China Ser. A, 46 (2003), 506-515
##[5]
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]
A class of fractional order systems with not instantaneous impulses
A class of fractional order systems with not instantaneous impulses
en
en
This paper is concerned with a kind of fractional order systems with Caputo-Hadamard derivative (of order \(q\in\mathbb{C}\) and \(\Re(q)\in(1,2)\)) and not instantaneous impulses. The obtained result uncovers that there exists a general solution for these impulsive systems, which means that the state trajectory of these impulsive systems is non-unique, and it is expounded by a numerical example.
4398
4407
Xianmin
Zhang
School of Mathematics and statistics
Yangtze Normal University
China
z6x2m@126.com;XianminZhang@126.com
Fractional differential equations
impulsive fractional differential equations
not instantaneous impulses
general solution
state trajectory.
Article.32.pdf
[
[1]
S. Abbas, M. Benchohra, Impulsive partial hyperbolic functional differential equations of fractional order with statedependent delay, Fract. Calc. Appl. Anal., 13 (2010), 225-242
##[2]
S. Abbas, M. Benchohra, Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order, Nonlinear Anal. Hybrid Syst., 4 (2010), 406-413
##[3]
Y. Adjabi, F. Jarad, D. Baleanu, T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, J. Comput. Anal. Appl., 21 (2016), 661-681
##[4]
Y.-R. Bai, Hadamard fractional calculus for interval-valued functions, J. Comput. Complex. Appl., 3 (2017), 23-43
##[5]
D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus, Models and numerical methods, Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2012)
##[6]
J.-X. Cao, H.-B. Chen, Some results on impulsive boundary value problem for fractional differential inclusions, Electron. J. Qual. Theory Differ. Equ., 2011 (2011), 1-24
##[7]
Y. Y. Gambo, F. Jarad, D. Baleanu, T. Abdeljawad , On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2014 (2014), 1-12
##[8]
T.-L. Guo, K.-J. Zhang, Impulsive fractional partial differential equations, Appl. Math. Comput., 257 (2015), 581-590
##[9]
E. Hernández, D. O’Regan, On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 141 (2013), 1641-1649
##[10]
F. Jarad, T. Abdeljawad, D. Baleanu , Caputo-type modification of the Hadamard fractional derivatives , Adv. Difference Equ., 2012 (2012), 1-8
##[11]
S. Kailasavalli, D. Baleanu, S. Suganya, M. M. Arjunan, Exact controllability of fractional neutral integro-differential systems with state-dependent delay in Banach spaces, An. Ştiinţ. Univ. ”Ovidius” Constana Ser. Mat., 24 (2016), 29-55
##[12]
A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[13]
P.-L. Li, C.-J. Xu, Mild solution of fractional order differential equations with not instantaneous impulses, Open Math., 13 (2015), 436-443
##[14]
M. Pierri, D. O’Regan, V. Rolnik, Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses , Appl. Math. Comput., 219 (2013), 6743-6749
##[15]
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##[16]
I. Stamova, G. Stamov, Stability analysis of impulsive functional systems of fractional order, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 702-709
##[17]
Y.-S. Tian, Z.-B. Bai, Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Comput. Math. Appl., 59 (2010), 2601-2609
##[18]
J.-R. Wang, Y.-R. Zhang, On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Lett., 39 (2015), 85-90
##[19]
J.-R. Wang, Y. Zhou, Z. Lin, On a new class of impulsive fractional differential equations, Appl. Math. Comput., 242 (2014), 649-657
##[20]
G.-C. Wu, D. Baleanu, Chaos synchronization of the discrete fractional logistic map, Signal Process., 102 (2014), 96-99
##[21]
G.-C. Wu, D. Baleanu, Discrete fractional logistic map and its chaos, Nonlinear Dynam., 75 (2014), 283-287
##[22]
G.-C. Wu, D. Baleanu, H.-P. Xie, F.-L. Chen, Chaos synchronization of fractional chaotic maps based on the stability condition, Phys. A, 460 (2016), 374-383
##[23]
X.-M. Zhang, On the concept of general solution for impulsive differential equations of fractional-order \(q \in (1, 2)\), Appl. Math. Comput., 268 (2015), 103-120
##[24]
X.-M. Zhang, The general solution of differential equations with Caputo-Hadamard fractional derivatives and impulsive effect, Adv. Difference Equ., 2015 (2015), 1-16
##[25]
X.-M. Zhang, X.-Z. Zhang, Z.-H. Liu, H. Peng, T. Shu, S.-Y. Yang, The general solution of impulsive systems with Caputo-Hadamard fractional derivative of order \(q \in \mathbb{C}(Re(q) \in (1, 2))\), Math. Probl. Eng., 2016 (2016), 1-20
##[26]
X.-M. Zhang, X.-Z. Zhang, M. Zhang, On the concept of general solution for impulsive differential equations of fractional order \(q \in (0, 1)\), Appl. Math. Comput., 247 (2014), 72-89
]
Solutions of nonlinear systems by reproducing kernel method
Solutions of nonlinear systems by reproducing kernel method
en
en
A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field.
4408
4417
Ali
Akgül
Department of Mathematics, Art and Science Faculty
Siirt University
Turkey
aliakgul00727@gmail.com
Yasir
Khan
Department of Mathematics
University of Hafr Al-Batin
Saudi Arabia
yasirmath@yahoo.com
Esra Karatas
Akgül
Gelibolu Piri Reis Vocational School
Canakkale Onsekiz Mart University
Turkey
esrakaratas@comu.edu.tr
Dumitru
Baleanu
Department of Mathematics and Computer Sciences, Art and Science Faculty
Department of Mathematics
Cankaya University
Institute of Space Sciences
Turkey
Romania
Maysaa Mohamed
Al Qurashi
Department of Mathematics
King Saud University
Saudi Arabia
Maysaa@ksu.edu.sa
Reproducing kernel method
series solutions
nonlinear systems.
Article.33.pdf
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[1]
G. T. Adams, N. S. Feldman, P. J. McGuire, Tridiagonal reproducing kernels and subnormality, J. Operator Theory, 70 (2013), 477-494
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A. H. Bhrawy, M. A. Abdelkawy, E. M. Hilal, A. A. Alshaery, A. Biswas, Solitons, cnoidal waves, snoidal waves and other solutions to Whitham-Broer-Kaup system, Appl. Math. Inf. Sci., 8 (2014), 2119-2128
##[9]
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F.-Z. Geng, S. P. Qian, Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers, Appl. Math. Lett., 26 (2013), 998-1004
##[20]
M. Inc, E. Fendoglu, H. Triki, A. Biswas, Compactons and topological solitons of the Drinfel’d-Sokolov system, Nonlinear Anal. Model. Control, 19 (2014), 209-224
##[21]
Y. Jia, Y.-J. Zhang, G. Xu, X.-Y. Zhuang, T. Rabczuk, Reproducing kernel triangular B-spline-based FEM for solving PDEs, Comput. Methods Appl. Mech. Engrg., 267 (2013), 342-358
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W. Jiang, Z. Chen, Solving a system of linear Volterra integral equations using the new reproducing kernel method, Appl. Math. Comput., 219 (2013), 10225-10230
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M. T. Karaev, Erratum: Use of reproducing kernels and Berezin symbols technique in some questions of operator theory , [Forum Math., DOI 10.1515/FORM.2011.073] [ MR2926635], Forum Math., 25 (2013), 1-1107
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X.-Y. Li, B.-Y. Wu, Reproducing kernel method for singular multi-point boundary value problem, Math. Sci. (Springer), 6 (2012), 1-5
##[25]
X.-Y. Li, B.-Y. Wu, New algorithm for nonclassical parabolic problems based on the reproducing kernel method, Math. Sci. (Springer), 7 (2013), 1-5
##[26]
M. Mohammadi, R. Mokhtari, H. Panahipour, A Galerkin-reproducing kernel method: application to the 2D nonlinear coupled Burgers’ equations, Eng. Anal. Bound. Elem., 37 (2013), 1642-1652
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J. Niu, Y.-Z. Lin, M.-G. Cui, A novel approach to calculation of reproducing kernel on infinite interval and applications to boundary value problems, Abstr. Appl. Anal., 2013 (2013), 1-7
##[28]
K. Özen, K. Oruçoğlu, Approximate solution to a multi-point boundary value problem involving nonlocal integral conditions by reproducing kernel method, Math. Model. Anal., 18 (2013), 529-536
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K. R. Rajagopal, On boundary conditions for fluids of the differential type, Navier-Stokes equations and related nonlinear problems, Funchal, (1994), Plenum, New York, 278 (1995), 273-278
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B.-H. Sheng, P.-X. Ye, The learning rates of regularized regression based on reproducing kernel Banach spaces, Abstr. Appl. Anal., 2013 (2013), 1-10
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S. B. Sontz, A reproducing kernel and Toeplitz operators in the quantum plane, Commun. Math., 21 (2013), 137-160
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S. Twareque Ali, F. Bagarello, J. Pierre Gazeau, Quantizations from reproducing kernel spaces, Ann. Physics, 332 (2013), 127-142
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Y.-L. Wang, T. Chaolu, Z. Chen, Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems, Int. J. Comput. Math., 87 (2010), 367-380
##[34]
Y.-L. Wang, S. Lu, F.-G. Tan, M.-J. Du, H. Yu, Solving a class of singular fifth-order boundary value problems using reproducing kernel Hilbert space method, Abstr. Appl. Anal., 2013 (2013), 1-6
##[35]
Y.-L. Wang, L.-J. Su, X.-J. Cao, X.-N. Li, Using reproducing kernel for solving a class of singularly perturbed problems, Comput. Math. Appl., 61 (2011), 421-430
##[36]
W.-Y. Wang, M. Yamamoto, B. Han, Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation, Inverse Problems, 29 (2013), 1-15
##[37]
B. Y. Wu, X. Y. Li, A new algorithm for a class of linear nonlocal boundary value problems based on the reproducing kernel method, Appl. Math. Lett., 24 (2011), 156-159
##[38]
S.-S. Xie, S.-Y. Heo, S.-C. Kim, G.-S. Woo, S.-C. Yi, Numerical solution of one-dimensional Burgers’ equation using reproducing kernel function, J. Comput. Appl. Math., 214 (2008), 417-434
##[39]
L.-H. Yang, H.-Y. Li, J.-R. Wang, Solving a system of linear Volterra integral equations using the modified reproducing kernel method, Abstr. Appl. Anal., 2013 (2013), 1-5
##[40]
H.-M. Yao, Y.-Z. Lin, Solving singular boundary-value problems of higher even-order, J. Comput. Appl. Math., 223 (2009), 703-713
##[41]
Y. F. Zhou, X. Q. Lü, Y. Y. Zhang, Solving a class of integral equations in a reproducing kernel space, (Chinese) Natur. Sci. J. Harbin Normal Univ., 22 (2006), 12-15
]
Smooth solutions for the $p$-order functional equation \(f(\varphi(x))=\varphi^p(f(x))\)
Smooth solutions for the $p$-order functional equation \(f(\varphi(x))=\varphi^p(f(x))\)
en
en
This paper deals with the \(p\)-order functional equation
\[\left\{
\begin{array}{ll}
f(\varphi(x))=\varphi^p(f(x)),\\
\varphi(0)=1, \quad -1\leq \varphi(x)\leq1 , \quad x\in[-1,1],
\end{array}
\right.
\]
where \(p\geq 2\) is an integer, \(\varphi^p\) is the \(p\)-fold iteration of
\(\varphi\), and \(f(x)\) is smooth odd function on
\([-1,1]\) and satisfies \(f(0)=0, -1<f^{'}(x)<0, (x\in[-1,1]).\)
Using constructive method, the existence of
unimodal-even-smooth solutions of the above equation on \([-1,1]\) can be proved.
4418
4429
Min
Zhang
College of Science
China University of Petroleum
P. R. China
zhangminmath@163.com
Jie
Rui
College of Science
China University of Petroleum
P. R. China
rjhygl@163.com
Functional equation
constructive method
unimodal-even-smooth solution.
Article.34.pdf
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]
Positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions
Positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions
en
en
In this paper, by virtue of fixed point index on cones, we obtain
two existence theorems of positive solutions for a system of
nonlinear semipositone fractional \(q\)-difference equations with
\(q\)-integral boundary conditions. Concave functions and nonnegative matrices are used to characterize the
coupling behavior of our nonlinearities.
4430
4440
Wei
Cheng
School of Mathematical Sciences
Chongqing Normal University
China
1375415619@qq.com
Jiafa
Xu
School of Mathematical Sciences
Chongqing Normal University
China
xujiafa292@sina.com
Yujun
Cui
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province
Ministry of Science and Technology
Shandong University of Science and Technology
China
China
cyj720201@163.com
q-difference equation
q-integral boundary conditions
fixed point index
positive solution
concave function.
Article.35.pdf
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R. A. C. Ferreira, Positive solutions for a class of boundary value problems with fractional q-differences, Comput. Math. Appl., 61 (2011), 367-373
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J. Henderson, R. Luca, Existence of positive solutions for a system of semipositone fractional boundary value problems, Electron. J. Qual. Theory Differ. Equ., 2016 (2016), 1-28
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V. Kac, P. Cheung, Quantum Calculus, Springer, New York (2002)
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A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
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W. Yang, Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions, Appl. Math. Comput., 244 (2014), 702-725
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K. Zhang, J. Xu, D. O’Regan, Positive solutions for a coupled system of nonlinear fractional differential equations, Math. Meth. Appl. Sci., 38 (2015), 1662-1672
]
Extinction in a nonautonomous system of Volterra integrodifferential equations
Extinction in a nonautonomous system of Volterra integrodifferential equations
en
en
A nonautonomous system of Volterra integrodifferential equations is studied in this paper. It is
shown that if the coefficients are continuous, bounded above and below by positive constants
and satisfy certain inequalities, then one of the components will be driven to extinction while
the other one will stabilize at the certain positive solution of a nonlinear single species model.
4441
4450
Meng
Hu
School of mathematics and statistics
Anyang Normal University
China
humeng2001@126.com
Lili
Wang
School of mathematics and statistics
Anyang Normal University
China
ay_wanglili@126.com
Extinction
nonautonomous
Volterra integrodifferential equation
global attractivity.
Article.36.pdf
[
[1]
S. Ahmad, On the nonautonomous Volterra-Lotka competition equations, Proc. Amer. Math. Soc., 117 (1993), 199-204
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S. Ahmad, Extinction of species in nonautonomous Lotka-Volterra systems, Proc. Amer. Math. Soc., 127 (1999), 2905-2910
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F. Chen, X. Liao, Z. Huang, The dynamic behavior of N-species cooperation system with continuous time delays and feedback controls, Appl. Math. Comput., 181 (2006), 803-815
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F. Montes de Oca, L. Perez, Extinction in nonautonomous competitive Lotka-Volterra systems with infinite delay, Nonlinear Anal., 75 (2012), 758-768
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]
Singular left-definite Hamiltonian systems in the Sobolev space
Singular left-definite Hamiltonian systems in the Sobolev space
en
en
This paper is devoted to construct Weyl's theory for the singular
left-definite even-order Hamiltonian systems in the corresponding
Sobolev space. In particular, it is proved that there exist at least
\(n\)-linearly independent solutions in the Sobolev space for the
\(2n\)-dimensional Hamiltonian system.
4451
4458
Ekin
Ugurlu
Department of Mathematics, Faculty of Arts and Sciences
Cankaya University
Turkey
ekinugurlu@cankaya.edu.tr
Kenan
Tas
Department of Mathematics, Faculty of Arts and Sciences
Cankaya University
Turkey
kenan@cankaya.edu.tr
Dumitru
Baleanu
Department of Mathematics, Faculty of Arts and Sciences
Institute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@cankaya.edu.tr
Hamiltonian system
left-definite problems
Weyl theory.
Article.37.pdf
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F. V. Atkinson, Discrete and continuous boundary problems, Mathematics in Science and Engineering, Academic Press, New York-London (1964)
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A. M. Krall, \(H^1\) convergence of Fourier integrals, Indian J. Pure Appl. Math., 26 (1995), 41-50
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A. M. Krall , Left-definite regular Hamiltonian systems, Math. Nachr., 174 (1995), 203-217
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L. L. Littlejohn, R. Wellman, On the spectra of left-definite operators, Complex Anal. Oper. Theory, 7 (2013), 437-455
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L. L. Littlejohn, Q. Wicks, Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator, J. Math. Anal. Appl., 444 (2016), 1-24
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H. D. Niessen, Singuläre S-Hermitesche Rand-Eigenwertprobleme, Manuscripta Math., 3 (1970), 35-68
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H. D. Niessen, Zum verallgemeinerten zweiten Weylschen Satz, (German) Arch. Math. (Basel), 22 (1971), 648-656
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H. D. Niessen, Greensche Matrix und die Formel von Titchmarsh-Kodaira für singuläre S-hermitesche Eigenwertprobleme, (German) J. Reine Angew. Math., 261 (1973), 164-193
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G.-L. Shi, R. Yan, Spectral theory of left definite difference operators, J. Math. Anal. Appl., 337 (2008), 116-122
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E. Uğurlu, Singular Dirac systems in the Sobolev space, Turk. J. Math., 41 (2017), 933-939
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E. Uğurlu, D. Baleanu, K. Tas, Regular fractional differential equations in the Sobolev space, Fract. Calc. Appl. Anal., 20 (2017), 810-817
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]
A simultaneous Bregman projection methods for solving mixed split equality problems and fixed point problems in \(p\)-uniformly convex and uniformly smooth Banach spaces
A simultaneous Bregman projection methods for solving mixed split equality problems and fixed point problems in \(p\)-uniformly convex and uniformly smooth Banach spaces
en
en
In this article, a simultaneous Bregman projection scheme is introduced to approximate a common element of the set of fixed points of left Bregman strongly nonexpansive mapping and the set of solutions of mixed split equality problems in \(p (p\geq 2)\)-uniformly convex and uniformly smooth Banach spaces. We obtain the weak convergence theorem of the sequences generated by our scheme under some appropriate conditions. Furthermore, we apply our iterative algorithms to the split feasibility problem.
Finally, several numerical results are shown
to confirm the feasibility of the proposed methods. Our result presented in the article
are new and improve and extend some recent corresponding results.
4459
4473
Haitao
Che
School of Mathematics and Information Science
Weifang University
China
haitaoche@163.com
Meixia
Li
School of Mathematics and Information Science
Weifang University
China
limeixia001@163.com
JingJing
Tan
School of Mathematics and Information Science
Weifang University
China
tanjngjing1108@163.com
Fixed point
split equality problem
left Bregman strongly nonexpansive mapping
simultaneous iterative method
weak convergence
uniformly convex
uniformly smooth.
Article.38.pdf
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Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 15-50
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A. Moudafi, Alternating CQ-algorithms for convex feasibility and split fixed-point problems, J. Nonlinear Convex Anal., 15 (2014), 809-818
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B. Qu, N.-H. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Problems, 51 (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., 5 (2008), 1218-1229
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S. Reich, Book Review: Geometry of Banach spaces, duality mappings and nonlinear problems, Bull. Amer. Math. Soc. (N.S.), 26 (1992), 367-370
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S. Reich, A weak convergence theorem for the alternating method with Bregman distances, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York, 178 (1996), 313-318
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F. Schöpfer, Iterative regularization method for the solution of the split feasibility problem in Banach spaces, PhD thesis, Saarbrücken, Germany (2007)
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F. Schöpfer, T. Schuster, A. Louis, An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems, 24 (2008), 1-20
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H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16 (1991), 1127-1138
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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
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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
]
A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials
A numerical investigation on the structure of the zeros of the degenerate Euler-tangent mixed-type polynomials
en
en
In this paper, we obtain a general symmetric identity involving the degenerate Euler-tangent mixed-type polynomials and sums of generalized falling factorials.
We use this identity to describe some combinatorial relations between these polynomials and generalized factorial alternating sums.
Finally, we observe an interesting phenomenon of "scattering" of the zeros
of degenerate Euler-tangent mixed-type polynomials.
4474
4484
Cheon Seoung
Ryoo
Department of Mathematics
Hannam University
Korea
ryoocs@hnu.kr
Degenerate Euler polynomials
degenerate tangent polynomials
degenerate Euler-tangent mixed-type polynomials
generalized falling factorials
generalized factorial alternating sums
Stirling numbers of the first kind.
Article.39.pdf
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[1]
M. Açikgöz, D. Erdal, S. Araci , A new approach to q-Bernoulli numbers and q-Bernoulli polynomials related to q- Bernstein polynomials, Adv. Difference Equ., 2010 (2010), 1-9
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L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51-88
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D. V. Dolgy, T. Kim, S.-H. Rim, S. H. Lee, Symmetry identities for the generalized higher-order q-Bernoulli polynomials under \(S_3\) arising from p-adic Volkenborn ingegral on \(\mathbb{Z}_p\), Proc. Jangjeon Math. Soc., 17 (2014), 645-650
##[4]
J. Y. Kang, C. S. Ryoo, A research on the some properties and distribution of zeros for Stirling polynomials, J. Nonlinear Sci. Appl., 9 (2016), 1735-1747
##[5]
T. K. Kim, Barnes’ type multiple degenerate Bernoulli and Euler polynomials, Appl. Math. Comput., 258 (2015), 556-564
##[6]
F. Qi, D. V. Dolgy, T. Kim, C. S. Ryoo, On the partially degenerate Bernoulli polynomials of the first kind, Glob. J. Pure Appl. Math., 11 (2015), 2407-2412
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C. S. Ryoo, Calculating zeros of the second kind Euler polynomials, J. Comput. Anal. Appl., 12 (2010), 828-833
##[8]
C. S. Ryoo, A note on the symmetric properties for the tangent polynomials, Int. J. Math. Anal. (Ruse), 7 (2013), 2575-2581
##[9]
C. S. Ryoo, A note on the tangent numbers and polynomials, Adv. Stud. Theoret. Phys., 7 (2013), 447-454
##[10]
C. S. Ryoo, A numerical investigation on the zeros of the tangent polynomials, J. Appl. Math. Inform., 32 (2014), 315-322
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C. S. Ryoo, Notes on degenerate tangent polynomials, Glob. J. Pure Appl. Math., 11 (2015), 3631-3637
##[12]
P. T. Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, J. Number Theory, 128 (2008), 738-758
]
Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions
Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions
en
en
In this paper, we derive a new integral identity concerning differentiable mappings defined on relative convex set. By using the obtained identity as an auxiliary result, we prove some new Simpson-like type inequalities for mappings whose absolute values of the first derivatives are relative semi-\((\alpha,m)\)-logarithmically convex. Several special cases are also discussed.
4485
4498
Chang
Zhou
Department of Mathematics, College of Science
China Three Gorges University
P. R. China
changzhouctgu@163.com
Cheng
Peng
Department of Mathematics, College of Science
China Three Gorges University
P. R. China
pengchengctgu@163.com
Tingsong
Du
Department of Mathematics, College of Science
China Three Gorges University
P. R. China
tingsongdu@ctgu.edu.cn
Relative semi-((\alpha
m)\)-logarithmically convex
Simpson’s inequality
Hölder’s inequality
Young inequality.
Article.40.pdf
[
[1]
M. U. Awan, M. A. Noor, M. V. Mihai, K. I. Noor, Two point trapezoidal like inequalities involving hypergeometric functions, Filomat, 31 (2017), 2281-2292
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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
##[3]
X.-S. Chen, Some properties of semi-E-convex functions, J. Math. Anal. Appl., 275 (2002), 251-262
##[4]
X.-S. Chen, Some properties of semi-E-convex function and semi-E-convex programming, The Eighth International Symposium on Operations Research and Its Applications, 2009 (2009), 1-7
##[5]
L. Chun, F. Qi, Inequalities of Simpson type for functions whose third derivatives are extended s-convex functions and applications to means, J. Comput. Anal. Appl., 19 (2015), 555-569
##[6]
S. S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones, 34 (2015), 323-341
##[7]
T.-S. Du, Y.-J. Li, Z.-Q. Yang, A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions, Appl. Math. Comput., 293 (2017), 358-369
##[8]
S. Hussain, S. Qaisar, Generalizations of Simpson’s type inequalities through preinvexity and prequasiinvexity, Punjab Univ. J. Math. (Lahore), 46 (2014), 1-9
##[9]
S. Hussain, S. Qaisar, More results on Simpson’s type inequality through convexity for twice differentiable continuous mappings, SpringerPlus, 2016 (2016), 1-9
##[10]
İ. İşcan, Hermite-Hadamard type inequalities for harmonically \((\alpha,m)\)-convex functions, Hacet. J. Math. Stat., 45 (2016), 381-390
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İ. İşcan, E. Set, M. E. Özdemir, On new general integral inequalities for s-convex functions, Appl. Math. Comput., 246 (2014), 306-315
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İ. Karabayir, M. Tunç, E. Yüksel, On some inequalities for functions whose absolute values of the second derivatives are \(\alpha-, m-,(\alpha,m)\)-logarithmically convex, Georgian Math. J., 22 (2015), 251-257
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A. Kashuri, R. Liko, Generalizations of Hermite-Hadamard and Ostrowski type inequalities for \(MT_m\)-preinvex functions, Proyecciones, 36 (2017), 45-80
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M. A. Latif, S. S. Dragomir, New integral inequalities of Hermite-Hadamard type for n-times differentiable s-logarithmically convex functions with applications, Miskolc Math. Notes, 16 (2015), 219-235
##[15]
M. A. Latif, S. S. Dragomir, E. Momoniat , On Hermite-Hadamard type integral inequalities for n-times differentiable mand \((\alpha,m)\)-logarithmically convex functions, Filomat, 30 (2016), 3101-3114
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Y.-J. Li, T.-S. Du, A generalization of Simpson type inequality via differentiable functions using extended \((s,m)_\phi\)-preinvex functions, J. Comput. Anal. Appl., 22 (2017), 613-632
##[17]
Y.-J. Li, T.-S. Du, B. Yu, Some new integral inequalities of Hadamard-Simpson type for extended (s,m)-preinvex functions, Ital. J. Pure Appl. Math., 36 (2016), 583-600
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M. A. Noor, M. U. Awan, K. I. Noor, On some inequalities for relative semi-convex functions, J. Inequal. Appl., 2013 (2013), 1-16
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M. A. Noor, K. I. Noor, M. U. Awan, Hermite-Hadamard inequalities for relative semi-convex functions and applications, Filomat, 28 (2014), 221-230
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M. A. Noor, K. I. Noor, M. U. Awan, New integral inequalities for relative geometrically semi-convex functions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 78 (2016), 161-172
##[21]
S. Qaisar, C. He, S. Hussain, A generalizations of Simpson’s type inequality for differentiable functions using \((\alpha,m)\)-convex functions and applications, J. Inequal. Appl., 2013 (2013), 1-13
##[22]
F. Qi, B.-Y. Xi, Some integral inequalities of Simpson type for \(GA-\varepsilon-\)convex functions, Georgian Math. J., 20 (2013), 775-788
##[23]
M. Z. Sarikaya, M. E. Kiris, Some new inequalities of Hermite-Hadamard type for s-convex functions, Miskolc Math. Notes, 16 (2015), 491-501
##[24]
M. Z. Sarikaya, E. Set, M. E. Özdemir, On new inequalities of Simpson’s type for s-convex functions, Comput. Math. Appl., 60 (2010), 2191-2199
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Y. Shuang, Y. Wang, F. Qi, Integral inequalities of Simpson’s type for \((\alpha,m)\)-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 6364-6370
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M. Tunç, Some Hadamard-like inequalities via convex and s-convex functions and their applications for special means, Mediterr. J. Math., 11 (2014), 1047-1059
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M. Tunç, Ç. Yildiz, A. Ekinci, On some inequalities of Simpson’s type via h-convex functions, Hacet. J. Math. Stat., 42 (2013), 309-317
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Y. Wang, S.-H. Wang, F. Qi , Simpson type integral inequalities in which the power of the absolute value of the first derivative of the integrand is s-preinvex, Facta Univ. Ser. Math. Inform., 28 (2013), 151-159
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S. Wu, On the weighted generalization of the Hermite-Hadamard inequality and its applications , Rocky Mountain J. Math., 39 (2009), 1741-1749
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S.-H. Wu, I. A. Baloch, İ. İşcan, On harmonically (p, h, m)-preinvex functions, J. Funct. Spaces, 2017 (2017), 1-9
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Y. Wu, F. Qi, D.-W. Niu, Integral inequalities of Hermite-Hadamard type for the product of strongly logarithmically convex and other convex functions, Maejo Int. J. Sci. Technol., 9 (2015), 394-402
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S.-H. Wu, B. Sroysang, J.-S. Xie, Y.-M. Chu, Parametrized inequality of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex, SpringerPlus, 2015 (2015), 1-9
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B.-Y. Xi, F. Qi, Integral inequalities of Simpson type for logarithmically convex functions, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 559-566
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Z.-Q. Yang, Y.-J. Li, T.-S. Du, A generalization of Simpson type inequality via differentiable functions using (s, m)-convex functions, Ital. J. Pure Appl. Math., 35 (2015), 327-338
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E. A. Youness, E-convex sets, E-convex functions, and E-convex programming, J. Optim. Theory Appl., 102 (1999), 439-450
]
Mazur-Ulam type theorems for fuzzy normed spaces
Mazur-Ulam type theorems for fuzzy normed spaces
en
en
In this paper, we provide Mazur-Ulam type results for (not necessarily surjective) maps preserving equality of fuzzy distance defined between two fuzzy normed spaces.
Our main goal is to study the additivity of such generalizations of fuzzy isometries.
As in the classical case, the fuzzy strict convexity of the target space will play an important role.
4499
4506
J. J.
Font
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
font@uji.es
J.
Galindo
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
jgalindo@uji.es
S.
Macario
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
macario@uji.es
M.
Sanchis
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC)
Universitat Jaume I
Spain
sanchis@uji.es
Mazur-Ulam theorem
fuzzy normed spaces
strict convexity.
Article.41.pdf
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[1]
C. Alegre, S. Romaguera, Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms, Fuzzy Sets and Systems, 161 (2010), 2181-2192
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T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), 687-705
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Approximation properties of solutions of a mean value type functional inequalities
Approximation properties of solutions of a mean value type functional inequalities
en
en
We will prove the generalized Hyers-Ulam stability theorems of
a mean value type functional equation, namely
\[f(x) - g(y) = (x-y) h(sx + sy),\] which arises from the mean
value theorem.
As an application of our results, we introduce a
characterization of quadratic polynomials.
4507
4514
Ginkyu
Choi
Department of Electronic and Electrical Engineering, College of Science and Technology
Hongik University
Republic of Korea
gkchoi@hongik.ac.kr
Soon-Mo
Jung
Mathematics Section, College of Science and Technology
Hongik University
Republic of Korea
smjung@hongik.ac.kr
Yang-Hi
Lee
Department of Mathematics Education
Gongju National University of Education
Republic of Korea
yanghi2@hanmail.net
Hyers-Ulam stability
generalized Hyers-Ulam stability
mean value type functional equation
characterization of quadratic polynomials.
Article.42.pdf
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A new Mittag-Leffler function undetermined coefficient method and its applications to fractional homogeneous partial differential equations
A new Mittag-Leffler function undetermined coefficient method and its applications to fractional homogeneous partial differential equations
en
en
In this paper, we develop a new application of the Mittag-Leffler function that will extend the application to fractional homogeneous differential equations, and propose a Mittag-Leffler function undetermined coefficient method. A new solution is constructed in power series. When a very simple ordinary differential equation is satisfied, no matter the original equation is linear or nonlinear, the method is valid, then combine the alike terms, compare the coefficient with identical powers, and the undetermined coefficient will be obtained. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided, and the solutions are in the form of generalized Mittag-Leffler function. The results reveal that the approach introduced here are very effective and convenient for solving homogeneous differential equations with fractional order.
4515
4523
YanQin
Liu
Institute of Soft Matter Mechanics, Department of Engineering Mechanics
School of Mathematical Sciences
Hohai University
Dezhou University
China
China
yqliumath@163.com
HongGuang
Sun
Institute of Soft Matter Mechanics, Department of Engineering Mechanics
Hohai University
China
shg@hhu.edu.cn
XiuLing
Yin
School of Mathematical Sciences
Dezhou University
China
yinxiuling@dzu.edu.cn
BaoGui
Xin
Nonlinear Science Center, College of Economics and Management
Shandong University of Science and Technology
China
xin@tju.edu.cn
Mittag-Leffler function
undetermined coefficient method
fractional homogeneous equation
Caputo derivative.
Article.43.pdf
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Spectral analysis of quantum Dirac systems
Spectral analysis of quantum Dirac systems
en
en
In this study, we establish the quantum calculus analogue of the classical
Dirac system. Moreover, we investigate the Jost solution, eigenvalues,
spectral singularities and some quantitative properties of the spectrum of
this new system.
4524
4531
Nihal
Yokus
Department of Mathematics
Karamanoglu Mehmetbey University
Turkey
nyokus@kmu.edu.tr
Nimet
Coskun
Department of Mathematics
Karamanoglu Mehmetbey University
Turkey
cannimet@kmu.edu.tr
Quantum equations
spectral analysis
spectral singularities.
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]
A class of differential inverse quasi-variational inequalities in finite dimensional spaces
A class of differential inverse quasi-variational inequalities in finite dimensional spaces
en
en
In this paper, we introduce and study a class of differential inverse quasi-variational inequalities in finite dimensional Euclidean spaces, which are closely related to the differential variational inequalities. By using two important theorems on differential inclusions, we first prove some existence theorems for Carathéodory weak solutions of the differential inverse quasi-variational inequality considered. Then, with the Euler computation method, we construct an Euler time-dependent scheme for solving the differential inverse quasi-variational inequality and prove a convergence result on the Euler time-dependent scheme constructed.
4532
4543
Wei
Li
Geomathematics Key Laboratory of Sichuan Province
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection
Chengdu University of Technology
P. R. China
P. R. China
lovelylw@126.com
Yi-Bin
Xiao
School of Mathematical Sciences
University of Electronic Science and Technology of China
P. R. China
xiaoyb9999@hotmail.com
Nan-Jing
Huang
Department of Mathematics
Sichuan University
P. R. China
nanjinghuang@hotmail.com
Yeol Je
Cho
Department of Mathematics Education and the RINS
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjchomath@gmail.com
Differential inverse quasi-variational inequality
Carathéodory weak solution
Euler time-stepping scheme.
Article.45.pdf
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Y.-B. Xiao, N.-J. Huang, Sub-super-solution method for a class of higher order evolution hemivariational inequalities, Nonlinear Anal., 71 (2009), 558-570
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Stability analysis for a class of nonlinear impulsive switched systems
Stability analysis for a class of nonlinear impulsive switched systems
en
en
In this note, we show a new sufficient condition for exponentially stability for a class of nonlinear impulsive switched systems. Based on the result obtained, an effective computational method is devised for the construction of switched linear stabilizing feedback controllers. Finally, a numerical example is given to illustrate the feasibility of the proposed methods. Compared with the results shown by Xu and Teo [H.-L. Xu, K. L. Teo, IEEE Trans. Automat. Control, \({\bf 55}\) (2010), 2429--2433], the form of our result is simpler and its computational cost is lower.
4544
4551
Yuming
Feng
Key Laboratory of Intelligent Information Processing and Control, School of Computer Science and Engineering
School of Mathematics and Statistics
Chongqing Three Gorges University
Chongqing Three Gorges University
P. R. China
P. R. China
yumingfeng25928@163.com
Limin
Zou
School of Mathematics and Statistics
Chongqing Three Gorges University
P. R. China
limin-zou@163.com
Zhengwen
Tu
School of Mathematics and Statistics
Chongqing Three Gorges University
P. R. China
tuzhengwen@163.com
Nonlinear impulsive switched systems
exponential stability
switched Lyapunov functions
linear matrix inequalities.
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J.-L. Wang, H.-N. Wu, T.-W. Huang, S.-Y. Ren, Pinning control strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., 27 (2016), 749-761
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J.-L. Wang, H.-N. Wu, T.-W. Huang, S.-Y. Ren, J.-G. Wu, Pinning control for synchronization of coupled reactiondiffusion neural networks with directed topologies, IEEE Trans. Syst., Man, Cybern., Syst., 46 (2016), 1109-1120
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J.-L. Wang, H.-N. Wu, T.-W. Huang, S.-Y. Ren, J.-G. Wu, Passivity of directed and undirected complex dynamical networks with adaptive coupling weights, IEEE Trans. Neural Netw. Learn. Syst., 28 (2017), 1827-1839
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F. Xu, L. Dong, D. Wang, X. Li, R. Rakkiyappan, Globally exponential stability of nonlinear impulsive switched systems, Math. Notes, 97 (2015), 803-810
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H.-L. Xu, K. L. Teo, Exponential stability with \(L_2\)-gain condition of nonlinear impulsive switched systems, IEEE Trans. Automat. Control, 55 (2010), 2429-2433
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