]>
2017
10
3
ISSN 2008-1898
433
Generalized coincidence theory for set-valued maps
Generalized coincidence theory for set-valued maps
en
en
This paper presents a coincidence theory for general classes of maps based on the notion of a \(\Phi\)-essential map (we will also
discuss \(\Phi\)-epi maps).
855
864
Donal
O'Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
Ireland
donal.oregan@nuigalway.ie
Essential maps
epi maps
coincidence points
homotopy.
Article.1.pdf
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D. O’Regan , Continuation methods based on essential and 0-epi maps, Acta Appl. Math., 54 (1998), 319-330
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D. O’Regan, Continuation theorems for acyclic maps in topological spaces, Commun. Appl. Anal., 13 (2009), 39-45
##[12]
D. O’Regan, Homotopy principles for d-essential acyclic maps, J. Nonlinear Convex Anal., 14 (2013), 415-422
##[13]
D. O’Regan, Coincidence points for multivalued maps based on \(\Phi\)-epi and \(\Phi\)-essential maps, Dynam. Systems Appl.,, 24 (2015), 143-154
##[14]
D. O’Regan, R. Precup, Theorems of Leray-Schauder type and applications, Series in Mathematical Analysis and Applications,http://www.isr-publications.com/admin/jnsa/articles/3576/edit Gordon and Breach Science Publishers, Amsterdam (2001)
]
Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials
Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials
en
en
This paper is devoted to present the approximate solutions with helping of an efficient numerical method for the nonlinear
coupled system of dynamical marriage model in the fractional of Riemann-Liouville sense (FDMM). The proposed system
describes the dynamics of love affair between a couple. The proposed method is dependent on the use of useful properties of the
operational matrices of Bernstein polynomials. The operational matrices for the fractional integration in the Riemann-Liouville
sense and the product are used to reduce FDMM to the solution of non-linear system of algebraic equations using Newton
iteration method. Numerical simulation is given to show the validity and the accuracy of the proposed algorithm. We introduce
a comparison with the obtained solution using Runge-Kutta method.
865
873
Mohamed M.
Khader
Department of Mathematics and Statistics, College of Science
Department of Mathematics, Faculty of Science
Al-Imam Mohammad Ibn Saud Islamic University (IMSIU)
Benha University
Saudi Arabia
Egypt
mohamed.khader@fsc.bu.edu.eg
Rubayyi T.
Alqahtani
Department of Mathematics and Statistics, College of Science
Al-Imam Mohammad Ibn Saud Islamic University (IMSIU)
Saudi Arabia
rtalqahtani@imamu.edu.sa
Fractional dynamical model of marriage
Riemann-Liouville fractional derivatives
operational matrix
Bernstein polynomials.
Article.2.pdf
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[1]
M. Alipour, D. Rostamy, Bernstein polynomials for solving Abel’s integral equation, J. Math. Comput. Sci., 3 (2011), 403-412
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M. M. Khader, On the numerical solutions for the fractional diffusion equation, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 2535-2542
##[7]
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M. M. Khader, T. S. EL Danaf, A. S. Hendy, A computational matrix method for solving systems of high order fractional differential equations, Appl. Math. Model., 37 (2013), 4035-4050
##[11]
M. M. Khader, A. S. Hendy, A numerical technique for solving fractional variational problems, Math. Methods Appl. Sci., 36 (2013), 1281-1289
##[12]
M. M. Khader, N. H. Sweilam, Singularly perturbed BVP to estimation of diaphragm deflection in MEMS capacitive microphone: an application of ADM, Appl. Math. Comput., 281 (2016), 214-222
##[13]
M. M. Khader, N. H. Sweilam, A. M. S. Mahdy, Numerical study for the fractional differential equations generated by optimization problem using Chebyshev collocation method and FDM, Appl. Math. Inf. Sci., 7 (2013), 2011-2018
##[14]
E. Kreyszig, Introductory functional analysis with applications, John Wiley & Sons, New York-London-Sydney (1978)
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T. C. Martin, L. L. Bumpass, Recent trends in marital disruption, Demography, 26 (1989), 37-51
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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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N. Ozalp, I. Koca, A fractional order nonlinear dynamical model of interpersonal relationships, Adv. Difference Equ., 2012 (2012 ), 1-7
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D. Rostamy, M. Alipour, H. Jafari, D. Baleanu, Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis, Rom. Rep. Phys., 65 (2013), 334-349
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D. Rostamy, K. Karimi, Bernstein polynomials for solving fractional heat- and wave-like equations, Fract. Calc. Appl. Anal., 15 (2012), 556-571
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N. H. Sweilam, M. M. Khader, A Chebyshev pseudo-spectral method for solving fractional-order integro-differential equations, ANZIAM J., 51 (2010), 464-475
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N. H. Sweilam, M. M. Khader, A. M. S. Mahdy, Numerical studies for solving fractional-order Logistic equation, Int. J. Pure Appl. Math., 78 (2012), 1199-1210
##[24]
N. H. Sweilam, M. M. Khader, A. M. Nagy, Numerical solution of two-sided space-fractional wave equation using finite difference method, J. Comput. Appl. Math., 235 (2011), 2832-2841
]
Hybrid steepest-descent methods for systems of variational inequalities with constraints of variational inclusions and convex minimization problems
Hybrid steepest-descent methods for systems of variational inequalities with constraints of variational inclusions and convex minimization problems
en
en
Two hybrid steepest-descent schemes (implicit and explicit) for finding a solution of the general system of variational
inequalities (in short, GSVI) with the constraints of finitely many variational inclusions for maximal monotone and inversestrongly
monotone mappings and a minimization problem for a convex and continuously Fréchet differentiable functional (in
short, CMP) have been presented in a real Hilbert space. We establish the strong convergence of these two hybrid steepestdescent
schemes to the same solution of the GSVI, which is also a common solution of these finitely many variational inclusions
and the CMP. Our results extend, improve, complement and develop the corresponding ones given by some authors recently in
this area.
874
901
Zhao-Rong
Kong
Economics Management Department
Shanghai University of Political Science and Law
China
kongzhaorong@163.com
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
cfwen@kmu.edu.tw
Hybrid steepest-descent method
system of variational inequalities
variational inclusion
monotone mapping.
Article.3.pdf
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[1]
A. E. Al-Mazrooei, A. Latif, J.-C. Yao, Solving generalized mixed equilibria, variational inequalities, and constrained convex minimization, Abstr. Appl. Anal., 2014 (2014 ), 1-26
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C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
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L.-C. Ceng, Q. H. Ansari, M.-M. Wong, J.-C. Yao, Mann type hybrid extragradient method for variational inequalities, variational inclusions and fixed point problems, Fixed Point Theory, 13 (2012), 403-422
##[5]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Relaxed extragradient iterative methods for variational inequalities, Appl. Math. Comput., 218 (2011), 1112-1123
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L.-C. Ceng, S.-M. Guu, J.-C. Yao, A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces, Comput. Math. Appl., 61 (2011), 2447-2455
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G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
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##[21]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[22]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[23]
I. Yamada , The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, Haifa, (2000), 473–504, Stud. Comput. Math., North-Holland, Amsterdam,8 (2001)
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Y.-H. Yao, R.-D. Chen, H.-K. Xu, Schemes for finding minimum-norm solutions of variational inequalities, Nonlinear Anal., 72 (2010), 3447-3456
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Y.-H. Yao, Y.-C. Liou, S. M. Kang, Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method, Comput. Math. Appl., 59 (2010), 3472-3480
##[26]
Y.-H. Yao, Y.-C. Liou, J.-C. Yao, Finding the minimum norm common element of maximal monotone operators and nonexpansive mappings without involving projection, J. Nonlinear Convex Anal., 16 (2015), 835-854
##[27]
Y.-H. Yao, M. A. Noor, Y.-C. Liou, Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities, Abstr. Appl. Anal., 2012 (2012 ), 1-9
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Y.-H. Yao, M. Postolache, Y.-C. Liou, Z.-S. Yao, Construction algorithms for a class of monotone variational inequalities, Optim. Lett., 10 (2016), 1519-1528
##[29]
L.-C. Zeng, S.-M. Guu, J.-C. Yao, Characterization of H-monotone operators with applications to variational inclusions, Comput. Math. Appl., 50 (2005), 329-337
]
Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems
Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems
en
en
In a real uniformly convex and uniformly smooth Banach space, we first prove a new path convergence theorem and
then present some new semi-implicit iterative schemes with errors which are proved to be convergent strongly to the common
element of the set of zero points of infinite m-accretive mappings and the set of fixed points of infinite nonexpansive mappings.
The superposition of perturbed operators are considered in the construction of the iterative schemes and new proof techniques
are employed compared to some of the recent work. Some examples are listed and computational experiments are conducted,
which guarantee the effectiveness of the proposed iterative schemes. Moreover, a kind of parabolic systems is exemplified, which
sets up the relationship among iterative schemes, nonlinear systems and variational inequalities.
902
921
Li
Wei
School of Mathematics and Statistics
Hebei University of Economics and Business
China
diandianba@yahoo.com
Ravi P.
Agarwal
Department of Mathematics
Department of Mathematics, Faculty of Science
Texas A & M University-Kingsville
King Abdulaziz University
USA
Saudi Arabia
Ravi.Agarwal@tamuk.edu
Yaqin
Zheng
College of Science
Agricultural University of Hebei
China
48390294@qq.com
M-accretive mapping
\(\tau_i\)-strongly accretive mapping
contractive mapping
\(\lambda_i\)-strictly pseudocontractive mapping
semi-implicit iterative scheme
parabolic systems.
Article.4.pdf
[
[1]
R. P. Agarwal, D. O’Regan, D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications, Topological Fixed Point Theory and Its Applications, Springer, New York (2009)
##[2]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.-K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), 1-9
##[3]
V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Translated from the Romanian, Editura Academiei Republicii Socialiste Romania, Bucharest; Noordhoff International Publishing, Leiden (1976)
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R. E. Bruck Jr., Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc., 179 (1973), 251-262
##[5]
L.-C. Ceng, Q. H. Ansari, S. Schaible, J.-C. Yao, Hybrid viscosity approximation method for zeros of m-accretive operators in Banach spaces, Numer. Funct. Anal. Optim., 33 (2012), 142-165
##[6]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Mann-type steepest-descent and modified hybrid steepest-descent methods for variational inequalities in Banach spaces, Numer. Funct. Anal. Optim., 29 (2008), 987-1033
##[7]
L.-C. Ceng, A. R. Khan, Q. H. Ansari, J.-C. Yao, Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces, Nonlinear Anal., 70 (2009), 1830-1840
##[8]
L.-C. Ceng, H.-K. Xu, J.-C. Yao, Strong convergence of an iterative method with perturbed mappings for nonexpansive and accretive operators, Numer. Funct. Anal. Optim., 29 (2008), 324-345
##[9]
H.-H. Cui, M.-L. Su, On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators, Appl. Math. Comput., 258 (2015), 67-71
##[10]
P. E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912
##[11]
Y.-L. Song, L.-C. Ceng, A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces, J. Global Optim., 57 (2013), 1327-1348
##[12]
W. Takahashi, Proximal point algorithms and four resolvents of nonlinear operators of monotone type in Banach spaces, Taiwanese J. Math., 12 (2008), 1883-1910
##[13]
S.-H. Wang, P. Zhang, Some results on an infinite family of accretive operators in a reflexive Banach space, Fixed Point Theory Appl., 2015 (2015 ), 1-11
##[14]
L. Wei, R. P. Agarwal, Iterative algorithms for infinite accretive mappings and applications to p-Laplacian-like differential systems, Fixed Point Theory Appl., 2016 (2016 ), 1-23
##[15]
L. Wei, R. P. Agarwal, P. Y. J. Wong, New method for the existence and uniqueness of solution of nonlinear parabolic equation, Bound. Value Probl., 2015 (2015 ), 1-18
##[16]
L.Wei, Y.-C. Ba, R. P. Agarwal, New ergodic convergence theorems for non-expansive mappings andm-accretive mappings, J. Inequal. Appl., 2016 (2016 ), 1-20
##[17]
L. Wei, R.-L. Tan, Iterative scheme with errors for common zeros of finite accretive mappings and nonlinear elliptic system, Abstr. Appl. Anal., 2014 (2014 ), 1-9
##[18]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[19]
H.-K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl., 314 (2006), 631-643
]
Positive and negative solutions of impulsive functional differential equations
Positive and negative solutions of impulsive functional differential equations
en
en
This paper considers the global existence of positive and negative solutions for impulsive functional differential equations
(IFDEs). First, we introduce the concept of "-unstability to IFDEs and establish some sufficient conditions to guarantee the
"-unstability via Lyapunov-Razumikhin method. Based on the obtained results, we present some sufficient conditions for the
global existence of positive and negative solutions of IFDEs. An example is also given to demonstrate the effectiveness of the
results.
922
928
Yanhui
Ding
School of Information Science and Engineering
Shandong Normal University
P. R. China
yanhuiding@126.com
Min
Chen
Zaozhuang Urban Utilities and Landscaping Bureau
P. R. China
Impulsive functional differential equations (IFDEs)
global existence
Lyapunov-Razumikhin method
positive solution
negative solution.
Article.5.pdf
[
[1]
G. Ballinger, X.-Z. Liu, Existence and uniqueness results for impulsive delay differential equations, Differential equations and dynamical systems, Waterloo, ON, (1997), Dynam. Contin. Discrete Impuls. Systems, 5 (1999), 579-591
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D. Baınov, P. S. Simeonov, Systems with impulse effect, Stability, theory and applications , Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York (1989)
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D. Baınov, P. S. Simeonov, Theory of impulsive differential equations: periodic solutions and applications, Longman, Harlow (1993)
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X.-L. Fu, B.-Q. Yan, Y.-S. Liu, Introduction of impulsive differential systems, Science Press, Beijing (2005)
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X.-D. Li, R. Rakkiyappan, G. Velmurugan, Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays, Inform. Sci., 294 (2015), 645-665
##[10]
X.-D. Li, S.-J. Song, Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays, IEEE Trans. Neural Netw. Learn. Syst., 24 (2013), 868-877
##[11]
X.-D. Li, J.-H. Wu, Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica J. IFAC, 64 (2016), 63-69
##[12]
X.-Z. Liu, G. Ballinger , Boundedness for impulsive delay differential equations and applications to population growth models , Nonlinear Anal., 53 (2003), 1041-1062
##[13]
X.-Z. Liu, Q. Wang, The method of Lyapunov functionals and exponential stability of impulsive systems with time delay, Nonlinear Anal., 66 (2007), 1465-1484
##[14]
X.-Z. Liu, Z.-G. Zhang , Uniform asymptotic stability of impulsive discrete systems with time delay, Nonlinear Anal., 74 (2011), 4941-4950
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J.-H. Shen, J.-R. Yan, Razumikhin type stability theorems for impulsive functional-differential equations, Nonlinear Anal., 33 (1998), 519-531
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I. Stamova, G. T. Stamov , Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics, J. Comput. Appl. Math., 130 (2001), 163-171
]
Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind
Sharp Stolarsky mean bounds for the complete elliptic integral of the second kind
en
en
In the article, we prove that the double inequality
\[25/16<\varepsilon(r)/S_{5/2,2}(1,\acute{r})<\pi/2,\]
holds for all \(r \in (0, 1)\) with the best possible constants \(25/16\) and \(\pi/2\), where \(\acute{r}=(1-r^2)^{1/2}, \varepsilon(r)=\int^{\pi/2}_0\sqrt{1-r^2\sin^2(t)}dt\) , is
the complete elliptic integral of the second kind and \(S_{p,q}(a,b)=[q(a^p-b^p)/(p(a^q-b^q))]^{1/(p-q)}\), is the Stolarsky mean of a
and b.
929
936
Zhen-Hang
Yang
School of Mathematics and Computation Sciences
Customer Service Center
Hunan City University
State Grid Zhejiang Electric Power Research Institute
China
China
yzhkm@163.com
Yu-Ming
Chu
School of Mathematics and Computation Sciences
Hunan City University
China
chuyuming2005@126.com
Xiao-Hui
Zhang
Department of Mathematics
Zhejiang Sci-Tech University
China
xiaohui.zhang@zstu.edu.cn
Gaussian hypergeometric function
complete elliptic integral
Stolarsky mean.
Article.6.pdf
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[1]
M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. (1964)
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R. W. Barnard, K. Pearce, K. C. Richards, A monotonicity property involving \(_3F_2\) and comparisons of the classical approximations of elliptical arc length, SIAM J. Math. Anal., 32 (2000), 403-419
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P. Czinder, Z. Páles, Minkowski-type inequalities for two variable Stolarsky means, Acta Sci. Math. (Szeged), 69 (2003), 27-47
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##[8]
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Extensions of Holder-type inequalities on time scales and their applications
Extensions of Holder-type inequalities on time scales and their applications
en
en
In this paper, we present some new extensions of Hölder-type inequalities on time scales via diamond-\(\alpha\) integral. Moreover,
the obtained results are used to generalize Minkowski’s inequality and Beckenbach-Dresher’s inequality on time scales.
937
953
Jing-Feng
Tian
College of Science and Technology
North China Electric Power University
P. R. China
tianjf@ncepu.edu.cn
Ming-Hu
Ha
School of Science
Hebei University of Engineering
P. R. China
mhhhbu@163.com
Hölder-type inequality
diamond-\(\alpha\) integral
time scales
Minkowski’s inequality
Beckenbach-Dresher’s inequality.
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On second-order differential subordinations for a class of analytic functions defined by convolution
On second-order differential subordinations for a class of analytic functions defined by convolution
en
en
Making use of the convolution operator we introduce a new class of analytic functions in the open unit disk and investigate
some subordination results.
954
963
Arzu
Akgül
Faculty of Arts and Sciences, Department of Mathematics
Kocaeli University
Turkey
akgul@kocaeli.edu.tr
Analytic functions
univalent function
differential subordination
convex function
Hadamard product
best dominant.
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Fixed point theorems for (L)-type mappings in complete CAT(0) spaces
Fixed point theorems for (L)-type mappings in complete CAT(0) spaces
en
en
In this paper, fixed point properties for a class of more generalized nonexpansive mappings called (L)-type mappings are
studied in geodesic spaces. Existence of fixed point theorem, demiclosed principle, common fixed point theorem of single-valued
and set-valued are obtained in the third section. Moreover, in the last section, \(\Delta\)-convergence and strong convergence theorems
for (L)-type mappings are proved. Our results extend the fixed point results of Suzuki’s results in 2008 and Llorens-Fuster’s
results in 2011.
964
974
Jing
Zhou
Department of Mathematics
Harbin Institute of Technology
P. R. China
zhoujinggirl@126.com
Yunan
Cui
Department of Mathematics
Harbin University of Science and Technology
P. R. China
cuiya@hrbust.edu.cn
(L)-type mappings
geodesic spaces
fixed point theorems
common fixed point theorems
three-step iteration scheme.
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]
Some results on a finite family of Bregman quasi-strict pseudo-contractions
Some results on a finite family of Bregman quasi-strict pseudo-contractions
en
en
The aim of this article is to establish a common fixed point theorem for a finite family of Bregman quasi-strict pseudocontractions
in a reflexive Banach space. Applications to equilibrium problems, variational inequality problems, and zero point
problems are provided.
975
989
Zi-Ming
Wang
Department of Foundation
Shandong Yingcai University
China
wangziming@ymail.com
Airong
Wei
School of Control Science and Engineering
Shandong University
China
weiairong@sdu.edu.cn
Bregman mapping
generalized projection
variational inequality
reflexivity
hybrid method.
Article.10.pdf
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]
New results for fractional differential equations with impulses via variational methods
New results for fractional differential equations with impulses via variational methods
en
en
By using variational methods and some critical points theorems, we establish some new results for the existence of infinitely
many of solutions for fractional order differential equations with impulses. In addition, one example is given to illustrate our
results.
990
1003
Peiluan
Li
School of Mathematics and Statistics
Henan University of Science and Technology
China
lpllpl_lpl@163.com
Hui
Wang
College of Information Engineering
Henan University of Science and Technology
China
wh@haust.edu.cn
Zheqing
Li
Network and Information Center
Henan University of Science and Technology
China
lzq@haust.edu.cn
Fractional differential equations
impulses
infinitely many solutions
critical points theorem.
Article.11.pdf
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]
Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination
Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination
en
en
The object of the present paper is to introduce and investigate new subclasses of the function class \(\Sigma\) of bi-univalent
functions defined in the open unit disk U, involving quasi subordination. The coefficients estimate \(|a_2|\) and \(|a_3|\) for functions in
these new subclasses are also obtained.
1004
1011
Obaid
Algahtani
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
obalgahtani@ksu.edu.sa
Univalent functions
bi-univalent functions
quasi-subordination
subordination.
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Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making problem
Hesitant triangular intuitionistic fuzzy information and its application to multi-attribute decision making problem
en
en
The concept of hesitant triangular intuitionistic fuzzy sets (HTIFSs) presented in this paper is based upon hesitant fuzzy sets
and triangular intuitionistic fuzzy numbers (TIFNs). We have developed some hesitant triangular intuitionistic fuzzy aggregation
operators and standardized hesitant triangular intuitionistic fuzzy aggregation operators. Inspired by Li et al. [D.-Q. Li, W.-
Y. Zeng, Y.-B. Zhao, Inform. Sci., 321 (2015), 103–115], the distance measures of hesitant triangular intuitionistic fuzzy sets
are given, in order to explore the applications of which we have proposed three methods of multi-attribute decision making
(MADM) problems, as well as analysis of the comparison between those methods, thus we give an example to illustrate these
methods’ applicability and availability.
1012
1029
Jianjian
Chen
Department of Mathematics
Nanchang University
P. R. China
18770084953@163.com
Xianjiu
Huang
Department of Mathematics
Nanchang University
P. R. China
xjhuangxwen@163.com
Hesitant triangular intuitionistic fuzzy sets
operators
distance measure
multi-attribute decision making.
Article.13.pdf
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]
F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces
F-HR-type contractions on (\(\alpha,\eta\))-complete rectangular b-metric spaces
en
en
The aim of this paper is to present some fixed point results for generalized Wardowski-type contractions in the framework
of (\(\alpha,\eta\))-complete rectangular b-metric spaces. We also derive certain fixed point results for generalized F-contractions in
rectangular b-metric spaces endowed with a graph or a partial order. Moreover, an illustrative example is presented to support
the obtained results.
1030
1043
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Vahid
Parvaneh
Department of Mathematics
Gilan-E-Gharb Branch, Islamic Azad University
Iran
zam.dalahoo@gmail.com
Badria A. S.
Alamri
Department of Mathematics
King Abdulaziz University
Saudi Arabia
baalamri@kau.edu.sa
Zoran
Kadelburg
Faculty of Mathematics
University of Belgrade
Serbia
kadelbur@matf.bg.ac.rs
b-metric space
rectangular metric space
Hardy-Rogers condition
F-contraction
admissible mappings
property P.
Article.14.pdf
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]
New dynamical behavior of two waves for (2+1)-dimensional Broer-Kaup equation
New dynamical behavior of two waves for (2+1)-dimensional Broer-Kaup equation
en
en
New exact solutions including periodic breather wave, kink breather wave and doubly breather wave solutions are obtained
for (2+1)D BK equation by using Painleve analysis, variable separation approach, the homoclinic test method and generalized
CK method via the linearization of equation, variable separation and equivalent transformation, respectively. The dynamical behavior
and interaction between different waves are investigated. These results enrich the dynamic features of higher dimensional
nonlinear system.
1044
1050
Ying
Jiang
School of Science
Southwest University of Science and Technology
P. R. China
xsjy2000@qq.com
Da-Quan
Xian
School of Science
Southwest University of Science and Technology
P. R. China
xiandaquan@swust.edu.cn
Zheng-De
Dai
School of Mathematics and Statistics
Yunnan University
P. R. China
zddai@ynu.edu.cn
Broer-Kaup equation
coincidence point
equivalent transformation
variable separation
generalized CK method
dynamical behavior.
Article.15.pdf
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[1]
C.-Q. Dai, X. Cen, S.-S. Wu, Exotic localized structures based on a variable separation solution of the (2 + 1)-dimensional higher-order Broer-Kaup system, Nonlinear Anal., 10 (2009), 259-261
##[2]
Z.-D. Dai, J. Liu, D.-L. Li, Applications of HTA and EHTA to YTSF equation, Appl. Math. Comput., 207 (2009), 360-364
##[3]
B.-J. Hong, D.-C. Lu, New soliton-like solutions to the (2 + 1)-dimensional Broer-Kaup equation with variable coefficients, J. At. Mol. Phys., 25 (2008), 130-134
##[4]
W.-H. Huang, Y.-L. Liu, Z.-M. Lu, Doubly periodic wave and folded solitary wave solutions for (2 + 1)-dimensional higher-order Broer-Kaup equation, Chaos Solitons Fractals, 31 (2007), 54-63
##[5]
S. Kumar, K. Singh, R. K. Gupta, Painlev analysis, Lie symmetries and exact solutions for (2 + 1)-dimensional variable coefficients Broer-Kaup equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1529-1541
##[6]
D.-S. Li, Some new exact solutions to the (2 + 1)-dimensional Broer-Kaup equation with variable coefficients, J. At. Mol. Phys., 21 (2004), 133-138
##[7]
B.-Q. Li, Y.-L. Ma, The non-traveling wave solutions and novel fractal soliton for the (2 + 1)-dimensional Broer-Kaup equations with variable coefficients, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 144-149
##[8]
D.-S. Li, H.-Q. Zhang, Some new types of multisoliton solutions for the (2 + 1)-dimensional higher-order Broer-Kaup system, Appl. Math. Comput., 152 (2004), 847-853
##[9]
S.-H. Ma, J.-P. Fang, Q.-B. Ren, Z. Yang, Chaotic behaviors of the (2 + 1)-dimensional generalized Breor—Kaup system, Chin. Phys. B, 21 (2012), 140-144
##[10]
S.-H. Ma, Q.-B. Ren, J.-P. Fang, C.-L. Zheng , Special soliton structures and the phenomena of fission and annihilation of solitons for the (2 + 1)-dimensional Broer-Kaup system with variable coefficients, (Chinese) Acta Phys. Sinica, 56 (2007), 6777-6783
##[11]
J.-Y. Qiang, S.-H. Ma, J.-P. Fang, Fusion and fission solitons for the (2 + 1)-dimensional generalized Breor-Kaup system, Chin. Phys. B, 19 (2010), 106-111
##[12]
J.-H. Tian, New variable separation solutions to the (2 + 1)-dimensional Broer-Kaup equation, Science Technology and Engineering, 7 (2007), 5018-5021
##[13]
H. Wang, Y.-H. Tian, Non-Lie symmetry groups and new exact solutions of a (2 + 1)-dimensional generalized Broer-Kaup system, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3933-3940
##[14]
Z. Yang, S.-H. Ma, J.-P. Fang, Chaotic solutions of (2 + 1)-dimensional Broek-Kaup equation with variable coefficients, Chin. Phys. B, 20 (2011), 33-37
##[15]
E. Yomba, Y.-Z. Peng , Fission, fusion and annihilation in the interaction of localized structures for the (2+1)-dimensional generalized Broer-Kaup system, Chaos Solitons Fractals, 28 (2006), 650-657
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J.-F. Zhang, P. Han, Generalized dromion structures of the (2 + 1)-dimensional Broer-Kaup equations, Chin. J. At. Mol. Phys., 18 (2001), 216-220
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J.-F. Zhang, P. Han, Localized coherent structures of the (2+1)-dimensional Broer-Kaup equations, (Chinese) Acta Phys. Sinica, 51 (2002), 705-711
##[18]
J.-F. Zhang, Y.-L. Liu, Localized coherent structures of the (2 + 1)-dimensional higher order Broer-Kaup equations, (Chinese) ; translated from Appl. Math. Mech., 23 (2002), 489–496, Appl. Math. Mech. (English Ed.), 23 (2002), 549-556
##[19]
J.-L. Zhang, Y.-M. Wang, M.-L. Wang, Z.-D. Fang, Exact solutions to the (2+1)-dimensional Broer-Kaup equation with variable coefficients, Chin. J. At. Mol. Phys., 20 (2003), 92-94
##[20]
S.-L. Zhang, B. Wu, S.-Y. Lou, Painlevé analysis and special solutions of generalized Broer-Kaup equations, Phys. Lett. A, 300 (2002), 40-48
##[21]
X.-Q. Zhao, D.-B. Tang, L.-M. Wang, Y.-M. Zhang, Some new soliton wave solutions for (2+1)-dimensional Broer-Kaup equations, (Chinese) Acta Phys. Sin., 52 (2003), 1827-1831
##[22]
C.-L. Zheng, H.-P. Zhu, L.-Q. Chen, Exact solution and semifolded structures of generalized Broer-Kaup system in (2 + 1)-dimensions, Chaos Solitons Fractals, 26 (2005), 187-194
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J.-M. Zhu, Z.-Y. Ma, New exact solutions to the (2 + 1)-dimensional Broer-Kaup equation, Chaos Solitons Fractals, 34 (2007), 476-481
##[24]
J.-M. Zhu, Z.-Y. Ma, C.-L. Zheng, Localized fractal structure of the (2+1)-dimensional Broer-Kaup equations, (Chinese) Acta Phys. Sinica, 53 (2004), 3248-3251
]
Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation
Existence and nonexistence of positive solutions for Dirichlet-type boundary value problem of nonlinear fractional differential equation
en
en
In this paper, we investigate the existence and nonexistence of positive solutions for nonlinear fractional differential equation
boundary value problem. By means of fixed-point theorems on a cone and the properties of Green function, some sufficient
criteria are established. Our results can be considered as an extension of some previous results.
1051
1063
Xinyi
Liu
School of Mathematics and Statistics
Northeast Normal University
P. R. China
liuxy394@nenu.edu.cn
Zhijun
Zeng
School of Mathematics and Statistics
Northeast Normal University
P. R. China
zthzzj@amss.ac.cn
Positive solution
fractional differential equation
boundary value problem
the Krasnoselskii fixed point theorem.
Article.16.pdf
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M. Al-Akaidi, Fractal speech processing, Cambridge University Press, Cambridge (2004)
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A. Babakhani, V. Daftardar-Gejji , Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 278 (2003), 434-442
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Z. B. Bai, H. S. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311 (2005), 495-505
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L. Bi, M. Bohner, M. Fan, Periodic solutions of functional dynamic equations with infinite delay, Nonlinear Anal., 68 (2008), 1226-1245
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D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609-625
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D.-Q. Jiang, C.-J. Yuan, The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application, Nonlinear Anal., 72 (2010), 710-719
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M. A. Krasnoselskiı, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron P., Noordhoff Ltd., Groningen (1964)
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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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I. Podlubny, Fractional differential equations, An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
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D. Ye, M. Fan, H.-Y. Wang, Periodic solutions for scalar functional differential equations, Nonlinear Anal., 62 (2005), 1157-1181
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Z.-J. Zeng, Existence and multiplicity of positive periodic solutions for a class of higher-dimension functional differential equations with impulses, Comput. Math. Appl., 58 (2009), 1911-1920
]
Multivariate contraction mapping principle with the error estimate formulas in locally convex topological vector spaces and application
Multivariate contraction mapping principle with the error estimate formulas in locally convex topological vector spaces and application
en
en
The purpose of this paper is to present the concept of multivariate contraction mapping in a locally convex topological
vector spaces and to prove the multivariate contraction mapping principle in such spaces. The neighborhood-type error estimate
formulas are also established. The results of this paper improve and extend Banach contraction mapping principle in the new
idea.
1064
1074
Yongchun
Xu
Department of Mathematics, College of Science
Hebei North University
China
hbxuyongchun@163.com
Jinyu
Guan
Department of Mathematics, College of Science
Hebei North University
China
guanjinyu2010@163.com
Yanxia
Tang
Department of Mathematics, College of Science
Hebei North University
China
sutang2016@163.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
Contraction mapping principle
locally convex
topological vector spaces
fixed point
error estimate formula.
Article.17.pdf
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[1]
A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., 72 (2010), 2238-2242
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D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464
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F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math., 30 (1968), 27-35
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T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. , 65 (2006), 1379-1393
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J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71 (2009), 3403-3410
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J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[8]
J. R. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 125 (1997), 2327-2335
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J. R. Jachymski, I. Jóźwik, Nonlinear contractive conditions: a comparison and related problems, Fixed point theory and its applications, Banach Center Publ., Polish Acad. Sci. Inst. Math., Warsaw, 77 (2007), 123-146
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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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P. Liu, Basis of topological vector spaces, (Chinese) Wuhan University Press, (2002)
##[13]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
##[14]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212
##[15]
D. O’Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252
##[16]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha -\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[17]
Y.-F. Su, A. Petruşel, J.-C. Yao, Multivariate fixed point theorems for contractions and nonexpansive mappings with applications, Fixed Point Theory Appl., 2016 (2016), 1-19
##[18]
Y.-F. Su, J.-C. Yao, Further generalized contraction mapping principle and best proximity theorem in metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-13
##[19]
Y.-X. Tang, J.-Y. Guan, P.-C. Ma, Y.-C. Xu, Y.-F. Su, Generalized contraction mapping principle in locally convex topological vector spaces, J. Nonlinear Sci. Appl., 9 (2016), 4659-4665
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F.-F. Yan, Y.-F. Su, Q.-S. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2012 (2012), 1-13
]
Cyclic quasi-contractions of Ćirić type in b-metric spaces
Cyclic quasi-contractions of Ćirić type in b-metric spaces
en
en
In this paper, we give a negative answer to the open question raised by Radenovic et al. [S. Radenović, T. Došenović, T.
A. Lampert, Z. Golubović, Appl. Math. Comput., 273 (2016), 155–164]. Namely, we give two examples which show that the set
of fixed points for cyclic quasi-contractive mappings of Ćirić type may be empty. Then, by using a new lemma, we give some
sufficient conditions for the existence of fixed point for cyclic and non-cyclic quasi-contractive mappings of Ćirić type in b-metric
spaces. In particular, we show that the condition of Fatou property in the result of Amini-Harandi [A. Amini-Harandi, Fixed
Point Theory, 15 (2014), 351–358] may be omitted.
1075
1088
Fei
He
School of Mathematical Sciences
Inner Mongolia University
China
hefei@imu.edu.cn
Xiao-Yue
Zhao
School of Mathematical Sciences
Inner Mongolia University
China
Yu-Qi
Sun
School of Mathematical Sciences
Inner Mongolia University
China
b-metric space
fixed point
cyclic quasi-contractions of Ćirić type
Fatou property.
Article.18.pdf
[
[1]
A. Amini-Harandi, Fixed point theory for quasi-contraction maps in b-metric spaces, Fixed Point Theory, 15 (2014), 351-358
##[2]
H. Aydi, M. F. Bota, E. Karapınar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-8
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A new Toeplitz inversion formula, stability analysis and the value
A new Toeplitz inversion formula, stability analysis and the value
en
en
In this paper, Toeplitz and Hankel inversion formulae are presented by the idea of skew cyclic displacement. A new Toeplitz
inversion formula can be denoted as a sum of products of skew circulant matrices and upper triangular Toeplitz matrices. A
new Hankel inversion formula can be denoted as a sum of products of skew left circulant matrices and upper triangular Toeplitz
matrices. The stability of their inverse formulae are discussed and their algorithms are given respectively. How the analogue of
our formulae lead to a more efficient way to solve the Toeplitz and Hankel linear system of equations are proposed.
1089
1097
Yanpeng
Zheng
Dept. of Information and Telecommunications Engineering
The University of Suwon
Korea
zhengyanpeng0702@sina.com
Zunwei
Fu
Dept. of Mathematics
The University of Suwon
Korea
fuzunwei@lyu.edu.cn
Sugoog
Shon
Dept. of Information and Telecommunications Engineering
The University of Suwon
Korea
sshon@suwon.ac.kr
Toeplitz matrix
skew circulant matrix
inverse
stability
displacement transform.
Article.19.pdf
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Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
en
en
In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the newly
suggested nonlocal fractional derivative with Mittag-Leffler kernel. Then, we obtain the related integration by parts formula.
We use the Q-operator to confirm our results. The related Euler-Lagrange equations are reported and one illustrative example
is discussed.
1098
1107
Thabet
Abdeljawad
Department of Mathematics and Physical Sciences
Prince Sultan University
Saudi Arabia
tabdeljawad@psu.edu.sa
Dumitru
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@cankaya.edu.tr
Fractional calculus
Mittag-Leffler function
fractional integration by parts
fractional Euler-Lagrange equations.
Article.20.pdf
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B. S. T. Alkahtani, Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89 (2016), 547-551
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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), 447-457
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]
On a modified degenerate Daehee polynomials and numbers
On a modified degenerate Daehee polynomials and numbers
en
en
The Daehee polynomials and numbers are introduced by Kim and Kim in [D. S. Kim, T. Kim, Appl. Math. Sci. (Ruse), 7
(2013), 5969–5976], and many interesting identities and properties of these polynomials have been found by many researchers.
In this paper, we consider the modified degenerated Daehee polynomials and derive some new and interesting identities and
properties of those polynomials.
1108
1115
Jin-Woo
Park
Department of Mathematics Education
Daegu University
Republic of Korea
a0417001@knu.ac.kr
Byung Moon
Kim
Department of Mechanical System Engineering
Dongguk University
Republic of Korea
kbm713@dongguk.ac.kr
Jongkyum
Kwon
Department of Mathematics Education and RINS
Gyeongsang National University
Republic of Korea
mathkjk26@gnu.ac.kr
p-adic invariant integral on \(\mathbb{Z}_p\)
degenerate Daehee polynomials
modified degenerate Daehee polynomials.
Article.21.pdf
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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
##[4]
D. V. Dolgy, T. Kim, H. I. Kwon, J. J. Seo, On the modified degenerate Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 26 (2016), 1-9
##[5]
D. V. Dolgy, T. Kim, J. J. Seo, On the symmetric identities of modified degenerate Bernoulli polynomials, Proc. Jangjeon Math. Soc., 19 (2016), 301-308
##[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, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory, 76 (1999), 320-329
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T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), 288-299
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T. Kim, q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys., 15 (2008), 51-57
##[10]
D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976
##[11]
D. S. Kim, T. Kim, Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, J. Inequal. Appl., 2014 (2014 ), 1-19
##[12]
D. S. Kim, T. Kim, Identities arising from higher-order Daehee polynomial bases, Open Math., 13 (2015), 196-208
##[13]
D. S. Kim, T. Kim, On degenerate Bell numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fs. Nat., Ser. A Mat., 111 (2017), 435-446
##[14]
D. S. Kim, T. Kim, T. Komatsu, S.-H. Lee, Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials, Adv. Difference Equ., 2014 (2014), 1-22
##[15]
T. Kim, D. S. Kim, T. Komatsu, S.-H. Lee, Higher-order Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, J. Nonlinear Convex Anal., 16 (2015), 1993-2015
##[16]
D. S. Kim, T. Kim, T. Komatsu, J.-J. Seo, Barnes-type Daehee polynomials, Adv. Difference Equ., 2014 (2014), 1-6
##[17]
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
##[18]
D. S. Kim, T. Kim, S.-H. Lee, J.-J. Seo, Higher-order Daehee numbers and polynomials, Int. J. Math. Anal. (Ruse), 8 (2014), 273-283
##[19]
D. S. Kim, T. Kim, J.-J. Seo, Higher-order Daehee polynomials of the first kind with umbral calculus, Adv. Stud. Contemp. Math. (Kyungshang), 24 (2014), 5-18
##[20]
T. Kim, Y. Simsek, Analytic continuation of the multiple Daehee q-l-functions associated with Daehee numbers, Russ. J. Math. Phys., 15 (2008), 58-65
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V. Kurt, Some relation between the Bernstein polynomials and second kind Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 43-48
##[22]
E.-J. Moon, J.-W. Park, S.-H. Rim, A note on the generalized q-Daehee numbers of higher order, Proc. Jangjeon Math. Soc., 17 (2014), 557-565
##[23]
H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math. (Kyungshang), 18 (2009), 41-48
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J.-W. Park, On the q-analogue of \(\lambda\)-Daehee polynomials, J. Comput. Anal. Appl., 19 (2015), 966-974
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S. Roman, The umbral calculus, Academic Press, New York (2005)
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J.-J. Seo, T. Kim, Some identities of symmetry for Daehee polynomials arising from p-adic invariant integral on \(\mathbb{Z}_p\), Proc. Jangjeon Math. Soc., 19 (2016), 285-292
##[27]
J.-J. Seo, S.-H. Rim, T. Kim, S.-H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc., 17 (2014), 1-9
]
Hermite-Hadamard type inequalities for operator convex functions on the co-ordinates
Hermite-Hadamard type inequalities for operator convex functions on the co-ordinates
en
en
In the paper, the concept of operator convexity on the co-ordinates is introduced and some new Hermite-Hadamard type
inequalities for operator convex functions on the co-ordinates are established.
1116
1125
ShuHong
Wang
College of Mathematics
Inner Mongolia University for the Nationalities
China
shuhong7682@163.com
Hermite-Hadamard type inequality
co-ordinated operator convex function.
Article.22.pdf
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M. Alomari, M. Darus, The Hadamard’s inequality for s-convex function of 2-variables on the co-ordinates, Int. J. Math. Anal. (Ruse), 2 (2008), 629-638
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S. S. Dragomir, On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775-788
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S. S. Dragomir, An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, JIPAM. J. Inequal. Pure Appl. Math., 3 (2002), 1-8
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S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, JIPAM. J. Inequal. Pure Appl. Math., 3 (2002), 1-8
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S. S. Dragomir, Hermite-Hadamard’s type inequalities for operator convex functions, Applied Mathematics and Computation, 218 (2011), 766-772
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S. S. Dragomir, S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687-696
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A. G. Ghazanfari, Some new Hermite-Hadamard type inequalities for two operator convex functions, ArXiv, 2012 (2012 ), 1-12
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A. G. Ghazanfari, The Hermite-Hadamard type inequalities for operator s-convex functions, J. Adv. Res. Pure Math., 6 (2014), 52-61
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F. Hansen, Operator convex functions of several variables, Publ. Res. Inst. Math. Sci., 33 (1997), 443-463
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F. Hansen, Operator monotone functions of several variables, Math. Inequal. Appl., 6 (2003), 1-17
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K.-C. Hsu, Some Hermite-Hadamard type inequalities for differentiable co-ordinated convex functions and applications, Adv. Pure Math., 4 (2014), 326-340
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K.-C. Hsu, Refinements of Hermite-Hadamard type inequalities for differentiable co-ordinated convex functions and applications, Taiwanese J. Math., 19 (2015), 133-157
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H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100-111
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E. Kikianty, Hermite-Hadamard inequality in the geometry of Banach spaces, PhD thesis, Victoria University (2010)
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M. A. Latif, M. Alomari, Hadamard-type inequalities for product two convex functions on the co-ordinates, Int. Math. Forum, 4 (2009), 2327-2338
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M. A. Latif, M. Alomari, On Hadmard-type inequalities for h-convex functions on the co-ordinates, Int. J. Math. Anal. (Ruse), 3 (2009), 1645-1656
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M. A. Latif, S. S. Dragomir, On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012 (2012 ), 1-13
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J. Pečarić, T. Furuta, J. MićićHot, Y. Seo, Mond-Pečarić method in operator inequalities, Inequalities for bounded selfadjoint operators on a Hilbert space, Monographs in Inequalities, ELEMENT, Zagreb (2005)
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M. Z. Sarıkaya, E. Set, M. E. Ozdemir, S. S. Dragomir, New some Hadamard’s type inequalities for co-ordinated convex functions, Tamsui Oxf. J. Inf. Math. Sci., 28 (2012), 137-152
]
Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities
Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities
en
en
In this paper, we introduce and analyze a hybrid steepest-descent viscosity algorithm for solving the triple hierarchical
variational inequality problem with constraints of two problems: one generalized mixed equilibrium problem and another
bilevel variational inequality problem in a real Hilbert space. Under mild conditions, the strong convergence of the iteration
sequences generated by the algorithm is established. Our results improve and extend the corresponding results in the earlier
and recent literature.
1126
1147
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University; and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics; and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
simplex_liou@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
cfwen@kmu.edu.tw
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Hybrid steepest-descent viscosity method
triple hierarchical variational inequality
generalized mixed equilibrium problem.
Article.23.pdf
[
[1]
P. N. Anh, J. K. Kim, L. D. Muu, An extragradient algorithm for solving bilevel pseudomonotone variational inequalities, J. Global Optim., 52 (2012), 627-639
##[2]
L.-C. Ceng, S. Al-Homidan, Q. H. Ansari, J.-C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math., 223 (2009), 967-974
##[3]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Iterative methods for triple hierarchical variational inequalities in Hilbert spaces, J. Optim. Theory Appl., 151 (2011), 489-512
##[4]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642
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L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
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]
Fractal generation method based on asymptote family of generalized Mandelbrot set and its application
Fractal generation method based on asymptote family of generalized Mandelbrot set and its application
en
en
Generalized Mandelbrot set (k-M set) is the basis of fractal analysis. This paper presents a novel method to generate k-M
set, which generates k-M set precisely by constructing its asymptote family. Correctness of the proposed method is proved
as well as computational complexity is researched. Further, application of the generation method is studied, which is used to
analyze distribution of boundary points and periodic points of k-M set. Finally, experiments have been implemented to evaluate
the theoretical results.
1148
1161
Shuai
Liu
College of Computer Science
Inner Mongolia University
China
Zheng
Pan
College of Computer Science
Inner Mongolia University
China
Weina
Fu
College of Computer and Information Engineering
Inner Mongolia Agricultural University
China
Xiaochun
Cheng
Department of Computer Science
Middlesex University
UK
x.cheng@mdx.ac.uk
Fractal generating method
generalized Mandelbrot set
asymptote family
boundary point
periodic point.
Article.24.pdf
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]
Some families of generalized complete and incomplete elliptic-type integrals
Some families of generalized complete and incomplete elliptic-type integrals
en
en
Analogous to the recent generalizations of the familiar beta and hypergeometric functions by Lin et al. [S.-D. Lin, H. M.
Srivastava, J.-C. Yao, Appl. Math. Inform. Sci., 9 (2015), 1731–1738], the authors introduce and investigate some general families
of the elliptic-type integrals for which the usual properties and representations are naturally and simply extended. The object of
the present paper is to study these generalizations and their relationships with generalized hypergeometric functions of one, two
and three variables. Moreover, the authors establish the Mellin transform formulas and various derivative and integral properties
and obtain several relations for special cases in terms of well-known higher transcendental functions and some infinite series
representations containing the Meijer G-function, the Whittaker function and the complementary error functions, as well as the
Laguerre polynomials and the products thereof. A number of (known or new) special cases and consequences of the main results
presented here are also considered.
1162
1182
H. M.
Srivastava
Department of Mathematics and Statistics
Department of Medical Research, China Medical University Hospital
University of Victoria
China Medical University
Canada
Republic of China
harimsri@math.uvic.ca
R. K.
Parmar
Department of Mathematics
Government College of Engineering and Technology
India
rakeshparmar27@gmail.com
P.
Chopra
Department of Mathematics
Marudhar Engineering College
India
purnimachopra@rediffmail.com
Incomplete and complete elliptic integrals
generalized Beta function
generalized hypergeometric functions
generalized Appell functions
generalized Lauricella functions
Mellin transforms
Whittaker functions
Laguerre polynomials.
Article.25.pdf
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]
Results on soft continuous functions in the soft topological spaces equipped with soft Scott topology
Results on soft continuous functions in the soft topological spaces equipped with soft Scott topology
en
en
In this study, some properties of soft Scott topology are examined and some relations between soft Scott topology and
way below soft set relations are shown. Also the notion of soft Scott continuous function on soft topological spaces, which is
equipped with soft Scott topology, is defined by focusing on the structure of the continuity of soft function and some examples
are illustrated. Besides these, least fixed point theorem is proved for soft Scott continuous functions.
1183
1194
Gözde
Yaylali
Department of Mathematics, Faculty of Science
Muğla Sıtkı Kocman University
Turkey
gozdeyaylali@mu.edu.tr
Bekir
Tanay
Department of Mathematics, Faculty of Science
Muğla Sıtkı Kocman University
Turkey
btanay@mu.edu.tr
Soft set
soft topology
soft continuous function
soft Scott topology
least fixed point theorem.
Soft set
soft topology
soft continuous function
soft Scott topology
least fixed point theorem.
Article.26.pdf
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[1]
M. I. Ali, F. Feng, X.-Y. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553
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K. V. Babitha, J. J. Sunil, Soft set relations and functions, Comput. Math. Appl., 60 (2010), 1840-1849
##[3]
K. V. Babitha, J. J. Sunil, Transitive closures and ordering on soft sets, Comput. Math. Appl., 62 (2011), 2235-2239
##[4]
N. Çağman, S. Karataş, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011), 351-258
##[5]
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott, Continuous lattices and domains, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (2003)
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P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562
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##[9]
D.-W. Pei, D.-Q. Miao, From soft sets to information systems, 2005 IEEE International Conference on Granular Computing, 2 (2005), 617-621
##[10]
S. Roy, T. K. Samanta, An introduction of a soft topological spaces, Proceeding of UGC sponsored national seminar on recent trends in fuzzy set theory, rough set theory and soft set theory at Uluberia College on 23rd and 24th September, (2011), 9-12
##[11]
A. F. Sayed, Continuity of partially ordered soft sets via soft Scott topology and soft sobrification, Bull. Math. Sci. Appl., 9 (2014), 79-88
##[12]
B. Tanay, G. Yaylalı, New structures on partially ordered soft sets and soft Scott topology, Ann. Fuzzy Math. Inform., 7 (2014), 89-97
##[13]
B. Tanay, G. Yaylalı, Soft Way Below Relation, International Conference on Recent Advanced in Pure and Applied Mathematics, Antalya, Turkey (2014)
##[14]
D. Wardowski, On a soft mapping and its fixed points, Fixed Point Theory Appl., 2013 (2013), 1-11
##[15]
G. Yaylalı, B. Tanay, Intervals, Soft Ordered Topology and Some Results, National Mathematics Symposium UMS, (2014)
##[16]
G. Yaylalı, B. Tanay, Soft lattices and some results on orderings on soft set, J. Adv. Res. Pure Math., 7 (2015), 45-60
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G. Yaylalı, B. Tanay, Some new results on orderings on soft sets, J. Inst. Sci. Technol. Dumlupinar Univ., 34 (2015), 1-5
]
Applications of Mann's method to the split common fixed point problem
Applications of Mann's method to the split common fixed point problem
en
en
In the present paper, we suggest a new fixed point method for solving the split common fixed point problem of directed
operators. We present an iterative algorithm based on Mann’s method. We prove that the presented algorithm converges weakly
to a solution of the split common fixed point problem of directed operators.
1195
1200
Youli
Yu
School of Mathematics and Information Engineering
Taizhou University
China
yuyouli@tzc.edu.cn
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
China
yaozhsong@163.com
Yaqin
Wang
Department of Mathematics
Shaoxing University
China
wangyaqin0579@126.com
Xiaoli
Fang
Department of Mathematics
Shaoxing University
China
fxl0418@126.com
Split common fixed point problem
directed operator
weak convergence.
Article.27.pdf
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##[23]
Y.-H. Yao, L.-M. Leng, M. Postolache, X.-X. Zheng, Mann-type iteration method for solving the split common fixed point problem, J. Nonlinear Convex Anal., 18 (2017), 875-882
##[24]
Y.-H. Yao, Y.-C. Liou, T.-L. Lee, N.-C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal., 17 (2016), 655-668
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]
Fixed point results of Edelstein-Suzuki type multivalued mappings on b-metric spaces with applications
Fixed point results of Edelstein-Suzuki type multivalued mappings on b-metric spaces with applications
en
en
We obtain Edelstein-Suzuki type theorems for multivalued mappings in compact b-metric spaces. Moreover, we prove the
existence of coincidence and common fixed points of a hybrid pair of mappings that satisfies Edelstein-Suzuki type contractive
condition. We present some examples along with a comparison with results in existing literature. In the end, we present some
corollaries in the metric spaces with applications in best approximation theory.
1201
1214
H. A.
Alolaiyan
Mathematical Department
King Saud University
Saudi Arabia
holayan@ksu.edu.sa
B.
Ali
Department of Mathematics and Applied Mathematics
University of Pretoria
South Africa
basit.aa@gmail.com
M.
Abbas
Department of Mathematics
Department of Mathematics
University of Management and Technology
King Abdulaziz University
Pakistan
Saudi Arabia
abbas.mujahid@gmail.com
Edelstein-Suzuki
metric space
multivalued mapping
best approximations
fixed point.
Edelstein-Suzuki
metric space
multivalued mapping
best approximations
fixed point.
Article.28.pdf
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M. Abbas, L. Ćirić, B. Damjanović, M. A. Khan, Coupled coincidence and common fixed point theorems for hybrid pair of mappings, Fixed Point Theory Appl., 2012 (2012 ), 1-11
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]
Majorization by starlike functions
Majorization by starlike functions
en
en
The main object of this paper is to investigate some majorization problems involving the subclass \(S (\alpha,A, B)\) of starlike
functions in the open unit disk U. Relevant connections of the results presented here with those given by earlier workers on the
subject are also indicated.
1215
1220
Öznur Özkan
Kiliç
Department of Statistics and Computer Sciences
Başkent University
Turkey
oznur@baskent.edu.tr
Osman
Altıntaş
Department of Mathematics Education
Başkent University
Turkey
oaltintas@baskent.edu.tr
Analytic function
starlike function
convex function
subordination
majorization
Quasi-subordination.
Article.29.pdf
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[1]
A. Akgül, A new subclass of meromorphic functions defined by Hilbert space operator, Honam Math. J., 38 (2016), 495-506
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]
On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\)
On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\)
en
en
In this paper, we define and study the \(C\)-integral and strong \(C\)-integral of functions mapping a compact interval \(I_0\) of \(\mathbb{R}^m\)
into a real Banach space \(X\). We prove that the \(C\)-integral and strong \(C\)-integral are equivalent if and only if \(X\) is finite dimensional.
We also study the relations between the property \(S^*C\) and strong \(C\)-integral.
1221
1227
Dafang
Zhao
College of Science
School of Mathematics and Statistics
Hohai University
Hubei Normal University
P. R. China
P. R. China
dafangzhao@163.com
Jingjing
Wang
School of Information Science & Technology
Qingdao University of Science & Technology
P. R. China
kathy1003@163.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Informatics
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
\(C\)-integral
property \(S^*C\)
strong \(C\)-integral.
Article.30.pdf
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]
A new iterative scheme for finding attractive points of \((\alpha,\beta)\)-generalized hybrid set-valued mappings
A new iterative scheme for finding attractive points of \((\alpha,\beta)\)-generalized hybrid set-valued mappings
en
en
In this paper, we first introduce the notions of \((\alpha,\beta)\)-generalized hybrid set-valued mappings, strongly attractive points,
attractive points and condition \(\acute{I}\). Then we construct an iterative method for finding attractive points of \((\alpha,\beta)\)-generalized
hybrid set-valued mappings and obtain some convergence theorems of the proposed iterative scheme for \((\alpha,\beta)\)-generalized
hybrid set-valued mappings defined on a uniformly convex Banach space by using of condition \(\acute{I}\)and demi-compact property,
respectively.
1228
1237
Lili
Chen
Post Doctoral Station for Computer Science and Technology
Department of Mathematics
Harbin University of Science and Technology
Harbin University of Science and Technology
China
China
cll2119@hotmail.com
Lu
Gao
Department of Mathematics
Harbin University of Science and Technology
China
1048560048@qq.com
Yanfeng
Zhao
Department of Mathematics
Harbin University of Science and Technology
China
zhaoyanfeng@hrbust.edu.cn
Generalized hybrid set-valued mapping
strongly attractive point
attractive point
uniformly convex Banach space
condition \(\acute{I}\).
Article.31.pdf
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S. Dhompongsa, W. Inthakon, W. Takahashi, A weak convergence theorem for common fixed points of some generalized nonexpansive mappings and nonspreading mappings in a Hilbert space, Optimization, 60 (2011), 769-779
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S. Dhompongsa, A. Kaewkhao, B. Panyanak, On Kirk’s strong convergence theorem for multivalued nonexpansive mappings on CAT(0) spaces, Optimization, 75 (2012), 459-468
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S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45
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T. Domínguez Benavides, B. Gavira, Does Kirk’s theorem hold for multivalued nonexpansive mappings?, Fixed Point Theory Appl., 2010 (2010 ), 1-20
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E. Karapınar, P. Kumam, I. M. Erhan, Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-13
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P. Kocourek, W. Takahashi, J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math., 14 (2010), 2497-2511
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]
Oscillation of second-order difference equations
Oscillation of second-order difference equations
en
en
We obtain new oscillation theorems for a class of second-order linear difference equations. Our criteria complement and
improve related results reported in the literature. An illustrative example is given.
1238
1243
Ying
Huang
School of Mathematics
School of Mathematics and System Science
Jilin University
Shenyang Normal University
P. R. China
P. R. China
Jingjing
Wang
School of Information Science & Technology
Qingdao University of Science & Technology
P. R. China
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Informatics
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Oscillation
second-order
difference equation.
Article.32.pdf
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R. P. Agarwal, M. Bohner, S. R. Grace, D. O’Regan, Discrete oscillation theory, Hindawi Publishing Corporation, New York (2005)
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E. Thandapani, S. Selvarangam, R. Rama, M. Madhan, Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term, Fasc. Math., 56 (2016), 155-165
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J.-L. Yao, F.-W. Meng, Asymptotic behavior of solutions of certain higher order nonlinear difference equation, J. Comput. Appl. Math., 205 (2007), 640-650
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]
Solve the split equality problem by a projection algorithm with inertial effects
Solve the split equality problem by a projection algorithm with inertial effects
en
en
The split equality problem has wide applicability in many fields of applied mathematics. In this paper, by using the inertial
extrapolation, we introduce an inertial projection algorithm for solving the split equality problem. The weak convergence of
the proposed algorithm is shown. Finally, we present a numerical example to illustrate the efficiency of the inertial projection
algorithm.
1244
1251
Qiao-Li
Dong
Tianjin Key Laboratory for Advanced Signal Processing, College of Science
Civil Aviation University of China
China
dongql@lsec.cc.ac.cn
Dan
Jiang
Tianjin Key Laboratory for Advanced Signal Processing, College of Science
Civil Aviation University of China
China
danjiangmath@163.com
Split equality problem
projection algorithm
inertial extrapolation.
Article.33.pdf
[
[1]
F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space, SIAM J. Optim., 14 (2004), 773-782
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H. Attouch, J. Bolte, P. Redont, A. Soubeyran, Alternating proximal algorithms for weakly coupled convex minimization problems, Applications to dynamical games and PDE’s, J. Convex Anal., 15 (2008), 485-506
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H. Attouch, A. Cabot, F. Frankel, J. Peypouquet, Alternating proximal algorithms for linearly constrained variational inequalities: application to domain decomposition for PDE’s, Nonlinear Anal., 74 (2011), 7455-7473
##[4]
H. H. Bauschke, P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, With a foreword by Hédy Attouch, CMS Books in Mathematics/Ouvrages de Mathmatiques de la SMC, Springer, New York (2011)
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A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), 183-202
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C. Byrne, A. Moudafi, Extensions of the CQ algorithm for the split feasibility and split equality problems (10th draft), working paper or preprint, hal-00776640 (2012)
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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
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A. Chambolle, C. Dossal, On the convergence of the iterates of the ''fast iterative shrinkage/thresholding algorithm'', J. Optim. Theory. Appl., 166 (2015), 968-982
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Q.-L. Dong, Y.-J. Cho, L.-L. Zhong, T. M. Rassias, Inertial projection and contraction algorithms for variational inequalities, J. Global Optim., 2017 (2017), 1-18
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Q.-L. Dong, S.-N. He, Self-adaptive projection algorithms for solving the split equality problems, Fixed Point Theory, (accepted. ), -
##[11]
Q.-L. Dong, S.-N. He, J. Zhao, Solving the split equality problem without prior knowledge of operator norms, Optimization, 64 (2015), 1887-1906
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Q.-L. Dong, Y.-Y. Lu, J.-F. Yang, The extragradient algorithm with inertial effects for solving the variational inequality, Optimization, 65 (2016), 2217-2226
##[13]
Q.-L. Dong, H.-B. Yuan, Y.-J. Cho, T. M. Rassias, Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings, Optim. Lett., 2017 (2017 ), 1-6
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D. A. Lorenz, T. Pock, An inertial forward-backward algorithm for monotone inclusions, J. Math. Imaging Vision, 51 (2015), 311-325
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A. Moudafi, A relaxed alternating CQ-algorithm for convex feasibility problems, Nonlinear Anal., 79 (2013), 117-121
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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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A. Moudafi, E. Al-Shemas, Simultaneous iterative methods for split equality problem, Trans. Math. Program. Appl., 1 (2013), 1-11
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A. Moudafi, M. Oliny, Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math., 155 (2003), 447-454
##[19]
D.-L. Tian, L.-Y. Shi, R.-D. Chen, Iterative algorithm for solving the multiple-sets split equality problem with split selfadaptive step size in Hilbert spaces, J. Inequal. Appl., 2016 (2016 ), 1-9
]
Stability of additive-quadratic $\rho$-functional equations in Banach spaces: a fixed point approach
Stability of additive-quadratic $\rho$-functional equations in Banach spaces: a fixed point approach
en
en
Let
\[M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y),\\
M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y).\]
We solve the additive-quadratic \(\rho\)-functional equations
\begin{eqnarray}
M_1f(x,y):=\rho M_2f(x,y), \qquad\qquad (1)
\end{eqnarray}
and
\begin{eqnarray}
M_2f(x,y):=\rho M_1f(x,y), \qquad\qquad (2)
\end{eqnarray}
where \(\rho\) is a fixed nonzero number with \(\rho\neq 1\).
Using the fixed point method, we prove the Hyers-Ulam stability of the additive-quadratic \(\rho\)-functional equations (1) and
(2) in Banach spaces.
1252
1262
Choonkil
Park
Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
Sang Og
Kim
Department of Mathematics
Hallym University
Republic of Korea
sokim@hallym.ac.kr
Cihangir
Alaca
Department of Mathematics
Celal Bayar University
Turkey
cihangiralaca@yahoo.com.tr
Hyers-Ulam stability
fixed point method
additive-quadratic \(\rho\)-functional equation
Banach space.
Article.34.pdf
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Fixed point algorithms for the split problem of demicontractive operators
Fixed point algorithms for the split problem of demicontractive operators
en
en
A fixed point method is introduced for solving the split common fixed point problem of demicontractive operators in
Hilbert spaces. By virtue of this fixed point method, we construct an iteration based on Mann’s method for solving the split
common fixed point problem of demicontractive operators. Weak convergence analysis is given under some mild assumptions.
1263
1269
Xiaoxue
Zheng
Department of Mathematics
Tianjin Polytechnic University
China
zhengxiaoxue1991@aliyun.com
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
China
yaoyonghong@aliyun.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization
Kaohsiung Medical University, and Department of Medical Research, Kaohsiung Medical University Hospital
Taiwan
simplex_liou@hotmail.com
Limin
Leng
Department of Mathematics
Tianjin Polytechnic University
China
lenglimin@aliyun.com
Split common fixed point
demicontractive operator
weak convergence.
Article.35.pdf
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H. Zegeye, N. Shahzad, Y.-H. Yao, Minimum-norm solution of variational inequality and fixed point problem in Banach spaces, Optimization, 64 (2015), 453-471
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Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces
Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces
en
en
In this paper, the implicit midpoint rule of asymptotically nonexpansive mapping in CAT(0) spaces is introduced. By the
viscosity approximation method, we prove that the proposed implicit iteration converges strongly to a fixed point of asymptotically
nonexpansive mapping under certain assumptions imposed on the sequence of parameters. The results presented in the
paper improve and extend various results in the existing literature.
1270
1280
Yi
Li
School of Science
Southwest University of Science and Technology
China
liyi@swust.edu.cn
Hongbo
Liu
School of Science
Southwest University of Science and Technology
China
liuhongbo@swust.edu.cn
viscosity approximation methods
complete CAT(0) space
\(\Delta\)-convergence
Asymptotically nonexpansive
implicit iteration.
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H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015 ), 1-12
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Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions
Uniqueness results for nonlinear fractional differential equations with infinite-point integral boundary conditions
en
en
In this paper, we consider a class of nonlinear fractional differential equations involving the Riemann-Liouville fractional
derivative with infinite-point integral boundary conditions. Our analysis relies on the fixed point index theory and \(u_0\)-positive
operator. An example is given for the illustration of the main work.
1281
1288
Suli
Liu
Department of Mathematics
Jilin University
P. R. China
liusl15@mails.jlu.edu.cn
Junpeng
Liu
Department of Mathematics
Jilin University
P. R. China
liujp14@mails.jlu.edu.cn
Qun
Dai
College of Science
Changchun University of Science and Technology
P. R. China
daiqun1130@163.com
Huilai
Li
Department of Mathematics
Jilin University
P. R. China
lihuilai@jlu.edu.cn
Fractional differential equations
infinite-point integral boundary condition
\(u_0\)-positive operator
fixed point index theory.
Article.37.pdf
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B. Ahmad, R. P. Agarwal, Some new versions of fractional boundary value problems with slit-strips conditions, Bound. Value Probl., 2014 (2014 ), 1-12
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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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Y.-J. Cui, Uniqueness of solution for boundary value problems for fractional differential equations, Appl. Math. Lett., 51 (2016), 48-54
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D.-J. Guo, Nonlinear integral equations, Shandong Science and Technology Press, Jinan (1987)
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
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S.-L. Liu, H.-L. Li, Q. Dai, Nonlinear fractional differential equations with nonlocal integral boundary conditions, Adv. Difference Equ., 2015 (2015 ), 1-11
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S.-L. Liu, H.-L. Li, Q. Dai, J.-P. Liu, Existence and uniqueness results for nonlocal integral boundary value problems for fractional differential equations, Adv. Difference Equ., 2016 (2016 ), 1-14
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J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado (Eds.), Advances in fractional calculus, Theoretical developments and applications in physics and engineering, Including papers from the Minisymposium on Fractional Derivatives and their Applications (ENOC-2005) held in Eindhoven, August 2005, and the 2nd Symposium on Fractional Derivatives and their Applications (ASME-DETC 2005) held in Long Beach, CA, September 2005, Springer, Dordrecht (2007)
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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. Nikolskiı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon (1993)
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W.-Z. Xie, J. Xiao, Z.-G. Luo, Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions, Appl. Math. Lett., 41 (2015), 46-51
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X.-Q. Zhang, Positive solutions for a class of singular fractional differential equation with infinite-point boundary value conditions, Appl. Math. Lett., 39 (2015), 22-27
]