]>
2017
10
6
ISSN 2008-1898
503
Asymptotically \(\jmath\)-Lacunary statistical equivalent of order $\alpha$ for sequences of sets
Asymptotically \(\jmath\)-Lacunary statistical equivalent of order $\alpha$ for sequences of sets
en
en
This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of
order \(\alpha\), where \(0 < \alpha \leq 1\), \(\jmath\)-statistically limit, and \(\jmath\)-lacunary statistical convergence for sequences of sets. Let \((X, \rho)\) be a metric
space and \(\theta\) be a lacunary sequence. For any non-empty closed subsets \(A_k, B_k \subseteq X\) such that \(d(x,A_k) > 0\) and \(d(x, B
_k) > 0\) for
each \(x \in X\), we say that the sequences \(\{A_k\}\) and \(\{B_k\}\)are Wijsman asymptotically \(\jmath\)-lacunary statistical equivalent of order \(\alpha\) to
multiple L, where \(0 < \alpha \leq 1\), provided that for each \(\varepsilon > 0\) and each \(x \in X\),
\[\{r\in \mathbb{N}: \frac{1}{h^\alpha_r}|\{k\in I_r: |d(x;A_k,B_k)-L|\geq\varepsilon\}|\geq\delta\}\in \jmath,\]
(denoted by \(\{A_k\}^{s\frac{1}{\theta}(\jmath_W)^\alpha}\{B_k\}\) ) and simply asymptotically \(\jmath\)-lacunary statistical equivalent of order \(\alpha\) if \(L = 1\). In addition, we
shall also present some inclusion theorems. The study leaves some interesting open problems.
2860
2867
Ekrem
Savaş
Istanbul Commerce University
Department of Mathematics
Turkey
ekremsavas@yahoo.com
Asymptotical equivalent
sequences of sets
ideal convergence
Wijsman convergence
\(\jmath\)-statistical convergence
\(\jmath\)-lacunary statistical convergence
statistical convergence of order \(\alpha\).
Article.1.pdf
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E. Savaş, On I-lacunary statistical convergence of order \(\alpha\) for sequences of sets, Filomat, 29 (2015), 1223-1229
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U. Ulusu, E. Savaş, An extension of asymptotically lacunary statistical equivalence set sequences, J. Inequal. Appl., 2014 (2014), 1-8
]
Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions
Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions
en
en
In this paper, we introduce notions of \((\alpha ,\mu)\)-generalized rational contraction conditions and investigate the existence of the
fixed point of such mappings on complete metric spaces. To illustrate our result we also construct an example.
2868
2878
Nantaporn
Chuensupantharat
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
King Mongkut’s University of Technology Thonburi (KMUTT)
Thailand
nantaporn.joy@mail.kmutt.ac.th
Poom
Kumam
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
Department of Medical Research
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkuts University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Arslan Hojat
Ansari
Department of Mathematics
Karaj Branch, Islamic Azad University
Iran
analsisamirmath2@gmail.com
Muhammad Usman
Ali
School of Natural Sciences, Department of Mathematics
National University of Sciences and Technology
Pakistan
muh_usman_ali@yahoo.com
\(\alpha\)-admissible
\(\mu\)-subadmissible
fixed point
\((\alpha ،\mu)\)-generalized multivalued rational contraction
pair \((F، h)\) upper class condition.
Article.2.pdf
[
[1]
M. U. Ali, T. Kamran, On (\(\alpha^*,\psi\) )-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 (2013), 1-7
##[2]
M. U. Ali, T. Kamran, E. Karapınar, A new approach to (\(\alpha,\psi\) )-contractive nonself multivalued mappings, J. Inequal. Appl., 2014 (2014), 1-9
##[3]
M. U. Ali, T. Kamran, E. Karapınar, (\(\alpha,\psi,\xi\))-contractive multivalued mappings, Fixed Point Theory Appl., 2014 (2014), 1-8
##[4]
M. U. Ali, T. Kamran, W. Sintunavarat, P. Katchang, Mizoguchi-Takahashi’s fixed point theorem with \(\alpha,\eta\) functions, Abstr. Appl. Anal., 2013 (2013), 1-4
##[5]
P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 519-526
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A. H. Ansari, Note on ”\(\alpha\)-admissible mappings and related fixed point theorems”, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, September , (2014), 373-376
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A. H. Ansari, S. Shukla, Some fixed point theorems for ordered F-(F, h)-contraction and subcontraction in 0-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), 37-53
##[8]
J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of \(\alpha-\psi\)-contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 1-6
##[9]
N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-23
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T. Kamran, Mizoguchi-Takahashi’s type fixed point theorem, Comput. Math. Appl., 57 (2009), 507-511
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E. Karapınar, R. Ali, T. Kamran, M. U. Ali, Generalized multivalued rational type contractions, , 9 (2016), 26-36
##[12]
E. Karapınar, B. Samet, Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 1-17
##[13]
Q. Kiran, M. U. Ali, T. Kamran, Generalization of Mizoguchi-Takahashi type contraction and related fixed point theorems, J. Inequal. Appl., 2014 (2014), 1-9
##[14]
G. Mınak, I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, J. Inequal. Appl., 2013 (2013), 1-10
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B. Mohammadi, S. Rezapour, On modified \(\alpha-\phi\)-contractions, J. Adv. Math. Stud., 6 (2013), 162-166
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B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 1-10
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S. Rezapour, M. E. Samei, Some fixed point results for \(\alpha-\psi\)-contractive type mappings on intuitionistic fuzzy metric spaces, J. Adv. Math. Stud., 7 (2014), 176-181
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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
]
Hopf bifurcation control of calcium oscillations in hepatocytes
Hopf bifurcation control of calcium oscillations in hepatocytes
en
en
This paper discusses a problem of the Hopf bifurcation control for a mathematical model of intracellular calcium oscillations
by calculating the curvature coefficient of limit cycle and the bifurcation control theory. We find that the appearance and
disappearance of calcium oscillations in this system are due to the supercritical and subcritical Hopf bifurcation of equilibrium
points, respectively. In addition, a nonlinear feedback controller is proposed to control the frequency and amplitude of periodic
orbits arising from the Hopf bifurcation. Numerical analysis and simulation results are carried out to illustrate the validity of
the feedback controller in controlling Hopf bifurcations.
2879
2885
Quanbao
Ji
School of Financial Science
Huainan Normal University
P. R. China
Hongkun
Zuo
School of Financial Science
Huainan Normal University
P. R. China
Yi
Zhou
School of Financial Science
Huainan Normal University
P. R. China
zhouyi3280@163.com
Calcium oscillations
control
Hopf bifurcation
curvature coefficient.
Article.3.pdf
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]
Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces
Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces
en
en
In this paper, we give some strong and weak convergence algorithms to find a common element of the solution set of a
split equilibrium problem and the fixed point set of a relatively nonexpansive mapping in Banach spaces. Our algorithms only
involve the operator \(A\) itself and do not need any conditions of the adjoint operator \(A^*\) of \(A\) and the norm \(\|A\|\) of \(A\) which are
different from the other results in the literature. By applying our main results, we show the existence of a solution of a split
feasibility problem in Banach spaces. Finally, we give an example to illustrate the main results of this paper
2886
2901
Baohua
Guo
Department of Mathematics and physics
North China Electric Power University
China
yanxialuncepu@163.com
Ping
Ping
Department of Mathematics and physics
North China Electric Power University
China
pingpingncepu@163.com
Haiqing
Zhao
Department of Mathematics and physics
North China Electric Power University
China
haiqingzhaoncepu@163.com
Yeol Je
Cho
Department of Mathematics Education and RINS
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjcho@gnu.ac.kr
Split equilibrium problem
equilibrium problem
fixed point
Article.4.pdf
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P. Kumam, P. Katchang, A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3 (2009), 475-486
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A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems, J. Nonlinear Convex Anal., 9 (2008), 37-43
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A. Moudafi, Split monotone variational inclusions, J. Optim Theory Appl., 150 (2011), 275-283
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S. Plubtieng, R. Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 336 (2007), 455-469
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S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings, Appl. Math. Comput., 197 (2008), 548-558
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X.-L. Qin, S. Y. Cho, S. M. Kang, Strong convergence of shrinking projection methods for quasi-\(\phi\)-nonexpansive mappings and equilibrium problems, J. Comput. Appl. Math., 234 (2010), 750-760
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X.-L. Qin, Y. J. Cho, S. M. Kang, Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal., 72 (2010), 99-112
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S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506-515
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S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal., 69 (2008), 1025-1033
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W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70 (2009), 45-57
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Y.-C. Tang, J.-G. Peng, L.-W. Liu, A cyclic algorithm for the split common fixed point problem of demicontractive mappings in Hilbert spaces, Math. Model. Anal., 17 (2012), 457-466
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S.-H. Wang, X.-Y. Gong, A. A. Abdou, Y. J. Cho, Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications, Fixed Point Theory Appl., 2016 (2016), 1-22
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]
On generalized convex contractions of type-2 in b-metric and 2-metric spaces
On generalized convex contractions of type-2 in b-metric and 2-metric spaces
en
en
In this paper, we present the notion of generalized convex contraction mapping of type-2, which includes the generalized
convex contraction (resp. generalized convex contraction of order-2) of Miandaragh et al. [M. A. Miandaragh, M. Postolache,
S. Rezapour, Fixed Point Theory Appl., 2013 (2013), 8 pages] and the convex contraction mapping of type-2 of Istrăţescu[V. I.
Istrăţescu, I, Libertas Math., 1 (1981), 151–163]. Utilizing this class of mappings, we establish approximate fixed point and fixed
point theorems in the setting of b-metric and 2-metric spaces.
2902
2913
M. S.
Khan
Department of Mathematics and Statistics
Sultan Qaboos University
Sultanate of Oman
mohammad@squ.edu.om
Y. M.
Singh
Department of Humanities and Basic Sciences
Manipur Institute of Technology
India
ymahenmit@rediffmail.com
G.
Maniu
Department of Computer Science, Information Technology, Mathematics and Physics,
Petroleum-Gas University of Ploieşti
Romania
maniugeorgeta@gmail.com
M.
Postolache
China Medical University
Department of Mathematics & Informatics
University ”Politehnica” of Bucharest
Taiwan
Romania
mihai@mathem.pub.ro
Approximate fixed point
fixed point
convex contraction
asymptotic regular
\(\alpha\)-admissible
b-metric and 2-metric spaces.
Article.5.pdf
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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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Extension of the fractional derivative operator of the Riemann-Liouville
Extension of the fractional derivative operator of the Riemann-Liouville
en
en
By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses
its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating
functions.
2914
2924
Dumitru
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@caankaya.edu.tr
Praveen
Agarwal
Department of Mathematics
Department of Mathematics
Anand International College of Engineering
University Putra Malaysia
Republic of India
Malaysia
goyal.praveen2011@gmail.com
Rakesh K.
Parmar
Department of Mathematics
Govt. College of Engineering and Technology
India
Maysaa M.
Alqurashi
Department of Mathematics
King Saud University
Saudi Arabia
maysaa@ksu.edu.sa
Soheil
Salahshour
Department of Computer Engineering
Mashhad Branch, IAU
Iran
soheilsalahshour@yahoo.com
Hypergeometric function of two and three variables
fractional derivative operator
generating functions
Mellin transform.
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Resolvent dynamical systems and mixed variational inequalities
Resolvent dynamical systems and mixed variational inequalities
en
en
In this paper, we use the dynamical systems technique to suggest and investigate some inertial proximal methods for solving
mixed variational inequalities and related optimization problems. It is proved that the convergence analysis of the proposed
methods requires only the monotonicity. Some special cases are also considered. Our method of proof is very simple as
compared with other techniques. Ideas and techniques of this paper may be extended for other classes of variational inequalities
and equilibrium problems.
2925
2933
Bandar
Bin-Mohsin
Department of Mathematics
King Saud University
Saudi Arabia
balmohsen@ksu.edu.s
Muhammad Aslam
Noor
Department of Mathematics
Department of Mathematics
King Saud University
COMSATS Institute of Information Technology
Saudi Arabia
Pakistan
noormaslam@gmail.com
Khalida Inayat
Noor
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
khalidanoor@hotmail.com
Rafia
Latif
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
rafialatif818@gmail.com
Variational inequalities
dynamical systems
inertial proximal methods
convergence.
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Optimal approximate solution theorems for Geraghty's proximal contractions in partially ordered sets via w-distances
Optimal approximate solution theorems for Geraghty's proximal contractions in partially ordered sets via w-distances
en
en
The purpose of this paper is to solve some global optimization problems for Geraghty type proximal contractions in
the setting of partially ordered sets with a metric by using a w-distance and an algorithm for determining such an optimal
approximate solution, also, we give some examples to illustrate our main results.
2934
2945
Chirasak
Mongkolkeha
Department of Mathematics, Statistics and Computer Sciences, Faculty of Liberal Arts and Science
Kasetsart University
Thailand
faascsm@ku.ac.th
Eunyoung
Kim
Department of Mathematics Education and the RINS
Gyeongsang National University
Korea
eunyoung328@daum.net
Yeol Je
Cho
Department of Mathematics Education and the RINS
Center for General Education
Gyeongsang National University
China Medical University
Korea
Taiwan
yjcho@gnu.ac.kr
Optimal approximate solution
best proximity point
Geraghty’s proximal contraction
generalized distances
w-distance.
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S. S. Basha, Discrete optimization in partially ordered sets, J. Global Optim., 54 (2012), 511-517
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J. Caballero, J. Harjani, K. Sadarangani, A best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl., 2012 (2012), 1-9
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Coupled best approximation theorems for discontinuous operators in partially ordered Banach spaces
Coupled best approximation theorems for discontinuous operators in partially ordered Banach spaces
en
en
In this paper, we first discuss properties of the cone in normed product spaces. As applications, we then derive some
coupled best approximation and coupled coincidence best approximation point results for discontinuous operators in partially
ordered Banach spaces. Some of our results generalize those obtained in earlier work.
2946
2956
Dezhou
Kong
College of Information Science and Engineering
School of Mathematical Sciences
Shandong Agricultural University
Qufu Normal University
China
China
dezhoukong@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University of Technology
China
Australia
mathlls@163.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University of Technology
Australia
Y.Wu@curtin.edu.au
Coupled fixed point
best approximation
metric projection
discontinuous operator
mixed monotone
Banach space.
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A composite iterative algorithm for accretive and nonexpansive operators
A composite iterative algorithm for accretive and nonexpansive operators
en
en
In this paper, we propose a one-step composite iterative algorithm for solving operator equations involving accretive and
nonexpansive operators. We obtain a weak convergence theorem for these nonlinear operators in the framework of 2-uniformly
smooth and uniformly convex Banach space.
2957
2965
Hengjun
Zhao
School of Science
Henan University of Engineering
China
zzzhaohj@outlook.com
Accretive operator
nonexpansive operator
uniformly smooth
zero point.
Article.10.pdf
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Some identities for umbral calculus associated with partially degenerate Bell numbers and polynomials
Some identities for umbral calculus associated with partially degenerate Bell numbers and polynomials
en
en
In this paper, we study partially degenerate Bell numbers and polynomials by using umbral calculus. We give some new
identities for these numbers and polynomials which are associated with special numbers and polynomial.
2966
2975
Taekyun
Kim
Department of Mathematics
Department of Mathematics
College of Science Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Hyuck-In
Kwon
Department of Mathematics
Kwangwoon University
Republic of Korea
sura@kw.ac.kr
Seog-Hoon
Rim
Department of Mathematics Education
Kyungpook National University
Republic of Korea
shrim@knu.ac.kr
Partially degenerate Bell polynomials
umbral calculus.
Article.11.pdf
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D. S. Kim, T. Kim, D. V. Dolgy, On partially degenerate Bell numbers and polynomials, Proc. Jangjeon Math. Soc., 20 (2017), 337-345
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]
The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings
The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings
en
en
In this paper, we study a split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings,
and propose some cyclic iterative schemes. Moreover we prove some strong convergence theorems. The results obtained
in this paper generalize and improve the recent ones announced by many others.
2976
2985
Yaqin
Wang
Department of Mathematics
Shaoxing University
China
wangyaqin0579@126.com
Tae-Hwa
Kim
Department of Applied Mathematics, College of Natural Sciences
Pukyong National University
Korea
taehwa@pknu.ac.kr
Xiaoli
Fang
Department of Mathematics
Shaoxing University
China
fxl0418@126.com
Huimin
He
School of Mathematics and Statistics
Xidian University
China
huiminhe@126.com
Split common fixed-point problem
demicontractive mapping
strong convergence
cyclic iterative scheme.
Article.12.pdf
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A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Problems, 26 (2010), 1-6
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Y.-Q. Wang, T. H. Kim, Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings, J. Nonlinear Sci. Appl., 10 (2017), 154-165
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F.-H. Wang, H.-K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal., 74 (2011), 4105-4111
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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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Y.-H. Yao, J. Wu, Y.-C. Liou, Regularized methods for the split feasibility problem, Abstr. Appl. Anal., 2012 (2012), 1-13
]
Existence results and Hyers-Ulam stability to a class of nonlinear arbitrary order differential equations
Existence results and Hyers-Ulam stability to a class of nonlinear arbitrary order differential equations
en
en
This paper is concerned with developing some conditions that reveal existing and stability analysis for solutions to a class
of differential equations with fractional order. The required conditions are obtained by applying the technique of degree theory
of topological type. The concerned problem is converted to the integral equation and then to operator equation, where the
operator is defined by \(T : C[0, 1] \rightarrow C[0, 1]\). It should be noted that the assumptions on nonlinear function \(f(t, u(t))\) does not
usually ascertain that the operator T being compact. Moreover, in this paper we also establish some conditions under which the
solution of the considered class is Hyers-Ulam stable and also satisfies the conditions of Hyers-Ulam-Rassias and generalized
Hyers-Ulam stability. Proper example is provided for the illustration of main results.
2986
2997
Poom
Kumam
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science
Department of Medical Research
King Mongkut’s University of Technology Thonburi (KMUTT)
King Mongkut’s University of Technology Thonburi (KMUTT)
China Medical University Hospital, China Medical University
Thailand
Thailand
Taiwan
poom.kum@kmutt.ac.th
Amjad
Ali
Department of Mathematics
University of Malakand
Pakistan
amjadalimna@yahoo.com
Kamal
Shah
Department of Mathematics
University of Malakand
Pakistan
kamalshah408@gmail.com
Rahmat Ali
Khan
Department of Mathematics
University of Malakand
Pakistan
rahmat_alipk@yahoo.com
Arbitrary order differential equations
topological degree theory
condensing mapping
existence results
stability analysis.
Article.13.pdf
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Z.-Y. Gao, X.-L. Yu, J.-R. Wang, Exp-type Ulam-Hyers stability of fractional differential equations with positive constant coefficient, Adv. Difference Equ., 2015 (2015), 1-14
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I. A. Rus, Ulam stabilities of ordinary differential equations in a Banach space, Carpathian J. Math., 26 (2010), 103-107
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K. Shah, R. A. Khan, Multiple positive solutions to a coupled systems of nonlinear fractional differential equations, SpringerPlus, 5 (2016), 1-20
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J.-R. Wang, L.-L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron. J. Qual. Theory Differ. Equ., 2011 (2011), 1-10
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##[29]
J.-R. Wang, Y. Zhou, W. Wei, Study in fractional differential equations by means of topological degree methods, Numer. Funct. Anal. Optim., 33 (2012), 216-238
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K. Wongkum, P. Chaipunya, P. Kumam, On the generalized Ulam-Hyers-Rassias stability of quadratic mappings in modular spaces without \(\Delta_2\)-conditions, J. Funct. Spaces, 2015 (2015), 1-6
]
An efficient finite difference scheme for the 2D sine-Gordon equation
An efficient finite difference scheme for the 2D sine-Gordon equation
en
en
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the
discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the nonlinear term, it
leads to a sequence of nonlinear coupled equations. We use a linear iteration algorithm, which can solve them efficiently, and the
contraction mapping property is also proven. Based on truncation errors of the numerical scheme, the convergence analysis in
the discrete \(l^2\)-norm is investigated in detail. Moreover, we carry out various numerical simulations, such as verifications of the
second order accuracy, tests of energy conservation and circular ring solitons, to demonstrate the efficiency and the robustness
of the proposed scheme.
2998
3012
Xiaorong
Kang
School of Science
Southwest University of Science and Technology
China
kangxiaorong@swust.edu.cn
Wenqiang
Feng
Department of Mathematics
University of Tennessee
USA
wfeng1@vols.utk.edu
Kelong
Cheng
School of Science
Southwest University of Science and Technology
China
zhengkelong@swust.edu.cn
Chunxiang
Guo
School of Business
Sichuan University
China
guocx70@163.com
invex set
conservative
difference scheme
linear iteration
convergence.
Article.14.pdf
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[1]
J. Argyris, M. Haase, J. C. Heinrich, Finite element approximation to two-dimensional sine-Gordon solitons, Comput. Methods Appl. Mech. Engrg. , 86 (1991), 1-26
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Z. Asgari, S. M. Hosseini, Numerical solution of two-dimensional sine-Gordon and MBE models using Fourier spectral and high order explicit time stepping methods, Comput. Phys. Commun., 184 (2013), 565-572
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A. G. Bratsos, A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation, Numer. Algorithms, 43 (2006), 295-308
##[4]
A. G. Bratsos, The solution of the two-dimensional sine-Gordon equation using the method of lines, J. Comput. Appl. Math., 206 (2007), 251-277
##[5]
W. Chen, W. Feng, C. Wang, S. Wise, A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations, ArXiv, 2016 (2016), 1-34
##[6]
K.-L. Cheng, W.-Q. Feng, S. Gottlieb, C. Wang, A Fourier pseudospectral method for the ”good” Boussinesq equation with second-order temporal accuracy, Numer. Methods Partial Differential Equations, 31 (2015), 202-224
##[7]
R. J. Cheng, K. M. Liew, Analyzing two-dimensional sine-Gordon equation with the mesh-free reproducing kernel particle Ritz method, Comput. Methods Appl. Mech. Engrg., 245/246 (2012), 132-143
##[8]
K.-L. Cheng, C. Wang, S. M. Wise, X.-Y. Yue, A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn- Hilliard equation and its solution by the homogeneous linear iteration method, J. Sci. Comput., 69 (2016), 1083-1114
##[9]
M.-R. Cui, High order compact alternating direction implicit method for the generalized sine-Gordon equation, J. Comput. Appl. Math., 235 (2010), 837-849
##[10]
M. Dehghan, A. Ghesmati, Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM), Comput. Phys. Comm., 181 (2010), 772-786
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M. Dehghan, D. Mirzaei, The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation, Comput. Methods Appl. Mech. Engrg., 197 (2008), 476-486
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R. Jiwari, S. Pandit, R. C. Mittal, Numerical simulation of two-dimensional sine-Gordon solitons by differential quadrature method, Comput. Phys. Commun., 183 (2012), 600-616
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X.-J. Yang, F. Gao, H. M. Srivastava, Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations, Comput. Math. Appl., 73 (2017), 203-210
##[26]
X.-J. Yang, J. A. Tenreiro Machado, D. Baleanu, C. Cattani, On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos, 26 (2016), 1-5
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K.-L. Zheng, J.-S. Hu, High-order conservative Crank-Nicolson scheme for regularized long wave equation, Adv. Difference Equ., 2013 (2013), 1-12
]
A high-accuracy conservative difference approximation for Rosenau-KdV equation
A high-accuracy conservative difference approximation for Rosenau-KdV equation
en
en
In this paper, we study the initial-boundary value problem of Rosenau-KdV equation. A conservative two level nonlinear
Crank-Nicolson difference scheme, which has the theoretical accuracy \(O(\tau^2 + h^4)\), is proposed. The scheme simulates two
conservative properties of the initial boundary value problem. Existence, uniqueness, and priori estimates of difference solution
are obtained. Furthermore, we analyze the convergence and unconditional stability of the scheme by the energy method.
Numerical experiments demonstrate the theoretical results.
3013
3022
Jinsong
Hu
School of Science
Xihua University
China
hujs7758@163.com
Jun
Zhou
School of Mathematics and Statistics
Yangtze Normal University
China
flzjzklm@126.com
Ru
Zhuo
School of Science
Xihua University
China
1436897060@qq.com
Rosenau-KdV equation
finite difference scheme
conservative
convergence
stability.
Article.15.pdf
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F. E. Browder , Existence and uniqueness theorems for solutions of nonlinear boundary value problems, Proc. Sympos. Appl. Math., Amer. Math. Soc., Providence, R.I., 17 (1965), 24-49
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K.-L. Cheng, W.-Q. Feng, S. Gottlieb, C. Wang, A Fourier pseudospectral method for the ”good” Boussinesq equation with second-order temporal accuracy, Numer. Methods Partial Differential Equations, 31 (2015), 202-224
##[4]
K.-L. Cheng, C. Wang, S. M. Wise, X.-Y. Yue, A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn- Hilliard equation and its solution by the homogeneous linear iteration method, J. Sci. Comput., 69 (2016), 1083-1114
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A. Esfahani, Solitary wave solutions for generalized Rosenau-KdV equation, Commun. Theor. Phys. (Beijing), 55 (2011), 396-398
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F. Gao, X.-J. Yang, Local fractional Euler’s method for the steady heat-conduction problem, Therm. Sci., 20 (2016), 1-735
##[11]
J.-S. Hu, B. Hu, Y.-C. Xu, C-N difference schemes for dissipative symmetric regularized long wave equations with damping term, Math. Probl. Eng., 2011 (2011), 1-16
##[12]
J.-S. Hu, Y.-C. Xu, B. Hu, Conservative linear difference scheme for Rosenau-KdV equation, Adv. Math. Phys., 2013 (2013), 1-7
##[13]
J.-S. Hu, K.-L. Zheng, Two conservative difference schemes for the generalized Rosenau equation, Bound. Value Probl., 2010 (2010), 1-18
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S. Li, L. Vu-Quoc, Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation, SIAM J. Numer. Anal., 32 (1995), 1839-1875
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K. Omrani, F. Abidi, T. Achouri, N. Khiari, A new conservative finite difference scheme for the Rosenau equation, Appl. Math. Comput., 201 (2008), 35-43
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X.-T. Pan, L.-M. Zhang, Numerical simulation for general Rosenau-RLW equation: an average linearized conservative scheme, Math. Probl. Eng., 2012 (2012), 1-15
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X.-T. Pan, L.-M. Zhang, On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation, Appl. Math. Model., 36 (2012), 3371-3378
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T.-C. Wang, B.-L. Guo, L.-M. Zhang, New conservative difference schemes for a coupled nonlinear Schrödinger system, Appl. Math. Comput., 217 (2010), 1604-1619
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X.-J. Yang, F. Gao, A new technology for solving diffusion and heat equations, Therm. Sci., 21 (2017), 133-140
##[26]
X.-J. Yang, F. Gao, H. M. Srivastava, Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations, Comput. Math. Appl., 73 (2017), 203-210
##[27]
L.-M. Zhang, A finite difference scheme for generalized regularized long-wave equation, Appl. Math. Comput., 168 (2005), 962-972
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]
The Yang Laplace transform- DJ iteration method for solving the local fractional differential equation
The Yang Laplace transform- DJ iteration method for solving the local fractional differential equation
en
en
In this paper, we propose the Yang Laplace transform- DJ iteration method, which is derived from coupling the Yang-
Laplace transform method with the DJ iteration method. The solution procedure for the local fractional differential equations
is given. And some test examples are given to show the accuracy and the validity of the proposed technique.
3023
3029
Yong-Ju
Yang
School of Mathematics and Statistics
Nanyang Normal University
P. R. China
tomjohn1007@126.com
Cai
Yang
Department of Computer and Information Technology
Nanyang Normal University
P. R. China
nyyc@163.com
Xiao-Feng
Jin
Mechanical and Electrical Engineering
Jiaozuo University
P. R. China
jxfeng369@163.com
Yang-Laplace transform method
Yang Laplace transform- DJ iteration method
local fractional calculus.
Article.16.pdf
[
[1]
D. Baleanu, H. K. Jassim, M. Al Qurashi, Approximate analytical solutions of Goursat problem within local fractional operators, J. Nonlinear Sci. Appl., 9 (2016), 4829-4837
##[2]
V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl., 316 (2006), 753-763
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H. Jafari, H. K. Jassim, F. Tchier, D. Baleanu, On the approximate solutions of local fractional differential equations with local fractional operators, Entropy, 18 (2016), 150-155
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J. Singh, D. Kumar, J. J. Nieto, A reliable algorithm for a local fractional Tricomi equation arising in fractal transonic flow, Entropy, 2016 (2016), 1-8
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X.-J. Yang, H. M. Srivastava, An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 29 (2015), 499-504
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Y. Zhang, H. M. Srivastava, M. C. Baleanu, Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow, Adv. Mech. Eng., 7 (2015), 1-5
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]
BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index
BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index
en
en
In this paper, we investigate the blow-up criterion of a smooth solution of the nematic liquid crystal flow in threedimensional
space. More precisely, We prove that if
\(\int^T_0(\|\omega\|^{\frac{2}{2-\alpha}}_{\dot{B}^{-\alpha}_{\infty,\infty}}+\|\nabla d\|^2_{\dot{B}^0_{\infty,\infty}})dt<\infty, 0<\alpha<2,\) then the solution \((u, d)\)
can be extended smoothly beyond \(t = T\).
3030
3037
Baoquan
Yuan
School of Mathematics and Information Science
Henan Polytechnic University
China
bqyuan@hpu.edu.cn
Chengzhou
Wei
School of Mathematics and Information Science
Henan Polytechnic University
China
jisuanwei@163.com
Nematic liquid crystal flow
blow-up criteria
regularity criteria
Besov space.
Article.17.pdf
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]
Six unified results for reducibility of the Srivastava's triple hypergeometric series \(H_A\)
Six unified results for reducibility of the Srivastava's triple hypergeometric series \(H_A\)
en
en
We aim to provide six unified results for reducibility of the Srivastava’s triple hypergeometric series \(H_A\). The results are
obtained with the help of generalizations of classical summation theorems due to Kummer, Gauss second and Bailey for the
series \(_2F_1\) which have recently been published. Our main findings are also shown to be specialized to yield several known
results.
3038
3045
Junesang
Choi
Department of Mathematics
Dongguk University
Republic of Korea
junesang@mail.dongguk.ac.kr
Arjun K.
Rathie
Department of Mathematics, School of Physical Sciences
Central University of Kerala
India
akrathie@cukerala.ac.in
Gamma function
hypergeometric function
generalized hypergeometric function
summation theorems
Appell’s function \(F_1\)
triple hypergeometric series \(H_A\).
Article.18.pdf
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Y. S. Kim, A. K. Rathie, J.-S. Choi, Summation formulas derived from the Srivastava’s triple hypergeometric series \(H_C\), Commun. Korean Math. Soc., 25 (2010), 185-191
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]
Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces
Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces
en
en
In this paper, we introduce an ergodic-type method for solving a system of split variational inclusion and fixed point
problems of a family of nonexpansive mappings with averaged resolvent operator. We prove that the sequence generated by the
proposed algorithm converges strongly to a common element of the set of solutions of a system of split variational inclusion
and the set of fixed points of a family of nonexpansive mappings in Hilbert spaces, from which the minimum norm solution
is deduced as a special case. Moreover, a numerical example is given to illustrate the operational reliability and convergence
of the presented method and results, which may be viewed as a refinement and improvement of the previously known results.
3046
3058
Dao-Jun
Wen
College of Mathematics and Statistics
Chongqing Technology and Business University
China
daojunwen@163.com
Yi-An
Chen
College of Mathematics and Statistics
Chongqing Technology and Business University
China
chenyian@ctbu.edu.cn
Ying-Ling
Lu
College of Mathematics and Statistics
Chongqing Technology and Business University
China
1376725290@qq.com
Split variational inclusion
nonexpansive mapping
ergodic-type iteration
fixed point
minimum norm solution.
Article.19.pdf
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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 Mathématiques de la SMC, Springer, New York (2011)
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A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl., 150 (2011), 275-283
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D.-J. Wen, Y.-A. Chen, Iterative methods for split variational inclusion and fixed point problem of nonexpansive semigroup in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 1-14
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H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
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L. Yang, F.-H. Zhao, J. K. Kim, Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-\(\phi\)-nonexpansive mappings in Banach spaces, Appl. Math. Comput., 218 (2012), 6072-6082
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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
]
Multiple weighted estimates for vector-valued commutators of multilinear square functions
Multiple weighted estimates for vector-valued commutators of multilinear square functions
en
en
Let \(T\) be the multilinear square function with a kernel of Dini’s type and \(T_q\) be the vector-valued version of \(T\). In this paper,
we obtain the weighted strong type and weighted end-point weak type estimates for the commutators of \(T_q\) respectively if the
kernels satisfies L log \(L^l\)-Dini type conditions.
3059
3066
Zengyan
Si
School of Mathematics and Information Science
Henan Polytechnic University
People’s Republic of China
zengyan@hpu.edu.cn
Multilinear square functions
vector-valued inequality
weights.
Article.20.pdf
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K. F. Andersen, R. T. John, Weighted inequalities for vector-valued maximal functions and singular integrals, Studia Math., 69 (1980), 19-31
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D. Cruz-Uribe, J. M. Martell, C. Pérez, Extrapolation from \(A_\infty\) weights and applications, J. Funct. Anal., 213 (2004), 412-439
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G. David, J. L. Journé, Une caractérisation des opérateurs intégraux singuliers bornés sur \(L^2(R^n)\), (French) [[A characterization of singular integral operators bounded on \(L^2(R^n)\)]], C. R. Acad. Sci. Paris Sér. I Math., 296 (1983), 761-764
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A. K. Lerner, S. Ombrosi, C. Pérez, R. H.Torres, R. Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón -Zygmund theory, Adv. Math., 220 (2009), 1222-1264
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S. Sato, K. Yabuta, Multilinearized Littlewood-Paley operators, Sci. Math. Jpn., 55 (2002), 447-453
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Z.-Y. Si, Q.-Y. Xue , Weighted estimates for commutators of vector-valued maximal multilinear operators, Nonlinear Anal., 96 (2014), 96-108
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Z.-Y. Si, Q.-Y. Xue, Multilinear square functions with kernels of Dini’s type, J. Funct. Spaces, 2016 (2016), 1-11
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]
Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator
Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator
en
en
In this work, we introduce a new subclass of bi-univalent functions under the \(D_{p,q}\) operator. By using the Faber polynomial
expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class.
3067
3074
Şahsene
Altinkaya
Department of Mathematics, Faculty of Arts and Science
Uludag University
Turkey
sahsene@uludag.edu.tr
Sibel
Yalçin
Department of Mathematics, Faculty of Arts and Science
Uludag University
Turkey
syalcin@uludag.edu.tr
Analytic functions
common fixed point
bi-univalent functions
Faber polynomials.
Article.21.pdf
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H. Airault, Symmetric sums associated to the factorization of Grunsky coefficients,Groups and symmetries, CRM Proc. Lecture Notes Amer. Math. Soc., Providence, RI, 47 (2007), 3-16
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H. Airault, Remarks on Faber polynomials, Int. Math. Forum, 3 (2008), 449-456
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H. Airault, H. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006), 179-222
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H. Airault, J.-G. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (2002), 343-367
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A. Akgül, A new subclass of meromorphic functions defined by Hilbert space operator, Honam Math. J., 38 (2016), 495-506
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Ş. Altınkaya, S. Yalçin, Initial coefficient bounds for a general class of biunivalent functions, Int. J. Anal., 2014 (2014), 1-4
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Ş. Altınkaya, S. Yalçin, Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., 6 (2015), 180-185
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M. Polatoğlu, Y. Kahramaner, Y. Polatoğlu, Close-to-convex functions defined by fractional operator, Appl. Math. Sci. (Ruse), 7 (2013), 2769-2775
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F. H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46 (1908), 253-281
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N. Magesh, J. Yamini, Coefficient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8 (2013), 1337-1344
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Q.-H. Xu, Y.-C. Gui, H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25 (2012), 990-994
]
Common fixed point theorems concerning F-contraction in b-metric-like spaces
Common fixed point theorems concerning F-contraction in b-metric-like spaces
en
en
In this work, some new types of F-contraction are introduced in partially ordered b-metric-like spaces and some common
fixed point theorems concerning F-contraction are investigated. Moreover, we give an example to illustrate the availability of the
obtained results.
3075
3086
Chunfang
Chen
Department of Mathematics
Nanchang University
P. R. China
ccfygd@sina.com
Huiling
Xue
Department of Mathematics
Nanchang University
P. R. China
1528548445@qq.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
b-metric-like spaces
common fixed point
fixed point
F-contraction.
Article.22.pdf
[
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M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
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D. Gopal, M. Abbas, D. K. Patel, C. Vetro, Fixed points of \(\alpha\)-type F-contractive mappings with an application to nonlinear fractional differential equation, Acta Math. Sci. Ser. B Engl. Ed., 36 (2016), 957-970
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H. Piri, P. Kumam, Wardowski type fixed point theorems in complete metric spaces, Fixed Point Theory Appl., 2016 (2016), 1-12
##[12]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
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D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 1 (2014), 146-155
]
A note on impulsive control of nonlinear systems with impulse time window
A note on impulsive control of nonlinear systems with impulse time window
en
en
In this paper, we present some sufficient conditions for the stability of nonlinear systems with impulse time window by
using some inequality techniques and results of matrix analysis. The proposed results are simpler than ones shown by Feng
et al. [Y.-M. Feng, C.-D. Li, T.-W. Huang, Neurocomputing, 193 (2016), 7–13]. Finally, several numerical examples are given to
show the effectiveness of our results.
3087
3098
Yuming
Feng
School of Mathematics and Statistics
Key Laboratory of Intelligent Information Processing and Control, School of Computer Science and Engineering
Chongqing Three Gorges University
Chongqing Three Gorges University
P. R. China
P. R. China
yumingfeng25928@163.com
Yang
Peng
School of Mathematics and Statistics
Chongqing Three Gorges University
P. R. China
peng_yang2011@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
Jinkui
Liu
School of Mathematics and Statistics
Key Laboratory of Intelligent Information Processing and Control, School of Computer Science and Engineering
Chongqing Three Gorges University
Chongqing Three Gorges University
P. R. China
P. R. China
liujinkui2006@126.com
Nonlinear systems
impulsive control
impulse time window.
Article.23.pdf
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H.-M. Wang, S.-K. Duan, C.-D. Li, L.-D. Wang, T.-W. Huang, Stability criterion of linear delayed impulsive differential systems with impulse time windows, Int. J. Control Autom. Syst., 14 (2016), 174-180
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X. Wang, C.-D. Li, T.-W. Huang, X.-M. Pan, Impulsive control and synchronization of nonlinear system with impulse time window, Nonlinear Dynam., 78 (2014), 2837-2845
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X. Wang, J.-Z. Yu, C.-D. Li, H. Wang, T.-W. Huang, J.-J. Huang, Robust stability of stochastic fuzzy delayed neural networks with impulsive time window, Neural Netw., 67 (2015), 84-91
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T. Yang, Impulsive control theory, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin (2001)
##[21]
X.-J. Yang, C.-D. Li, T.-W. Huang, Q.-K. Song, Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses, Appl. Math. Comput., 93 (2017), 416-422
##[22]
X.-S. Yang, J.-Q. Lu, Finite-time synchronization of coupled networks with Markovian topology and impulsive effects, IEEE Trans. Automat. Control, 61 (2016), 2256-2261
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D.-G. Yang, G.-Y. Qiu, C.-D. Li, Global exponential stability of memristive neural networks with impulse time window and time-varying delays, Neurocomputing, 171 (2016), 1021-1026
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W. Zhang, C.-D. Li, T.-W. Huang, Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays, Int. J. Biomath., 10 (2017), 1-19
##[27]
Y.-H. Zhou, C.-D. Li, T.-W. Huang, X. Wang, Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window, Neural Comput. Appl., 28 (2017), 775-782
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L.-M. Zou, Y.-M. Jiang, Estimation of the eigenvalues and the smallest singular value of matrices, Linear Algebra Appl., 433 (2010), 1203-1211
]
On a non-autonomous stochastic Lotka-Volterra competitive system
On a non-autonomous stochastic Lotka-Volterra competitive system
en
en
In this paper, we consider a general non-autonomous Lotka-Volterra competitive model with random perturbations. Sufficient
conditions for stochastic permanence and extinction are established. Particularly, when these conditions are applied to a
stochastic logistic equation, these conditions are sufficient and necessary. Some figures are also worked out to illustrate the main
results. Some recent results are extended. Moreover, our results reveal that different types of stochastic noises have different
effects on the permanence and extinction of the population.
3099
3108
Meiling
Deng
School of Mathematical Science
Huaiyin Normal University
P. R. China
hnudengmeiling@163.com
Competitive system
random perturbations
permanence
extinction.
Article.24.pdf
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A. Bahar, X.-R. Mao, Stochastic delay Lotka-Volterra model, J. Math. Anal. Appl., 292 (2004), 364-380
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M. Liu, C.-Z. Bai, Optimal harvesting of a stochastic delay competitive model, Discrete Contin. Dyn. Syst., 22 (2017), 1493-1508
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C. Zhu, G. Yin, On competitive Lotka-Volterra model in random environments, J. Math. Anal. Appl., 357 (2009), 154-170
]
Discussion on a coupled fixed point theorem for single-valued operators in b-metric spaces
Discussion on a coupled fixed point theorem for single-valued operators in b-metric spaces
en
en
In this note, an existence and uniqueness theorem of fixed points for single-valued mappings in partially ordered b-metric
spaces is established. As a corollary, the contraction constant for a coupled fixed point theorem obtained in a recent paper is
relaxed from \([0,\frac{1}{s} )\) to \([0, 1)\). Furthermore, a system of integral equation is also discussed.
3109
3114
Yanbin
Sang
Department of Mathematics
North University of China
China
syb6662004@163.com
Dongxia
Zhao
Department of Mathematics
North University of China
China
zhaodongxia6@sina.com
b-metric space
contractive condition
partial order
coupled fixed point
mixed monotone operator.
Article.25.pdf
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V. Berinde, Coupled fixed point theorems for \(\phi\)-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 75 (2012), 3218-3228
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P. Eloe, R. H. Liu, Upper and lower solutions for regime-switching diffusions with applications in financial mathematics, SIAM J. Appl. Math., 71 (2011), 1354-1373
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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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W. Kirk, N. Shahzad, Fixed point theory in distance spaces, Springer, Cham (2014)
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H. K. Nashine, Z. Kadelburg, Cyclic generalized \(\varphi\)-contractions in b-metric spaces and an application to integral equations, Filomat, 28 (2014), 2047-2057
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A. Roldán, J. Martínez-Moreno, C. Roldán, Y. J. Cho, Multidimensional fixed point theorems under (\(\psi,\phi\))-contractive conditions in partially ordered complete metric spa, J. Comput. Appl. Math., 273 (2015), 76-87
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A. Roldán, J. Martínez-Moreno, C. Roldán, E. Karapınar, Some remarks on multidimensional fixed point theorems, Fixed Point Theory, 15 (2014), 545-558
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B. Samet, E. Karapınar, H. Aydi, V. Ćojbašić Rajić, Discussion on some coupled fixed point theorems, Fixed Point Theory Appl., 2013 (2013), 1-12
]
Hyers-Ulam stability of Pielou logistic difference equation
Hyers-Ulam stability of Pielou logistic difference equation
en
en
We investigate Hyers-Ulam stability of the first order difference equation \(x_{i+1}=\frac{ax_i+b}{cx_i+d}\) , where \(ad - bc = 1, c \neq 0\) and
\(|a+d|>2\). It has Hyers-Ulam stability if the initial point \(x_0\) lies in some definite interval of \(\mathbb{R}\). The condition \(|a+d|>2\) implies
that the above recurrence is a natural generalization of Pielou logistic difference equation.
3115
3122
Soon-Mo
Jung
Mathematics Section, College of Science and Technology
Hongik University
Republic of Korea
smjung@hongik.ac.kr
Young Woo
Nam
Mathematics Section, College of Science and Technology
Hongik University
Republic of Korea
namyoungwoo@hongik.ac.kr
Hyers-Ulam stability
Pielou logistic difference equation
first order difference equation
linear fractional map
Verhulst-Pearl differential equation.
Article.26.pdf
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[1]
J. Brzdęk, K. Ciepliński, Z. Leśniak, On Ulam’s type stability of the linear equation and related issues, Discrete Dyn. Nat. Soc., 2014 (2014), 1-14
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J. Brzdęk, D. Popa, B. Xu, The Hyers-Ulam stability of nonlinear recurrences, J. Math. Anal. Appl., 335 (2007), 443-449
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S.-M. Jung, Hyers-Ulam stability of the first-order matrix difference equations, Adv. Difference Equ., 2015 (2015), 1-13
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S.-M. Jung, Y. W. Nam, On the Hyers-Ulam stability of the first-order difference equation, J. Funct. Spaces, 2016 (2016), 1-6
##[7]
S.-M. Jung, D. Popa, M. T. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, J. Global Optim., 59 (2014), 165-171
##[8]
S.-M. Jung, M. T. Rassias, A linear functional equation of third order associated with the Fibonacci numbers, Abstr. Appl. Anal., 2014 (2014), 1-7
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D. Popa, Hyers-Ulam-Rassias stability of a linear recurrence, J. Math. Anal. Appl., 309 (2005), 591-597
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S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers, New York-London (1960)
]
Global existence and attractors for the two-dimensional Burgers-Ginzburg- Landau equations
Global existence and attractors for the two-dimensional Burgers-Ginzburg- Landau equations
en
en
This paper investigates the periodic initial value problem for the two-dimensional Burgers-Ginzburg-Landau (2D Burgers-
GL) equations, which can be derived from the so-called modulated modulation equations (MME) that govern the dynamics of
the modulated amplitudes of some periodic critical modes. The well-posedness of the solutions and the global attractors for the
2D Burgers-GL equations are obtained via delicate a priori estimates, the Galerkin method, and operator semigroup method.
3123
3135
Changhong
Guo
School of Management
Guangdong University of Technology
P. R. China
cmchguo@gdut.edu.cn
Shaomei
Fang
Department of Mathematics
South China Agricultural University
P. R. China
fangsm90@163.com
invex set
well-posedness
global attractors
a priori estimates.
Article.27.pdf
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[1]
A. J. S. Al-Saif, A. Abdul-Hussein, Generating exact solutions of two-dimensional coupled Burgers equations by the first integral method, Res. J. Phys. Appl. Sci., 1 (2012), 29-33
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C.-H. Guo, S.-M. Fang, B.-L. Guo, Long time behavior of solutions to coupled Burgers-complex Ginzbury-Landau (Burgers-CGL) equations for flames governed by sequential reaction, [[Long time behavior of solutions to coupled Burgers-complex Ginzburg-Landau (Burgers-CGL) equations for flames governed by sequential reaction]] Appl. Math. Mech. (English Ed.), 35 (2014), 515-534
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Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces
Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces
en
en
Two implicit iterative algorithms are presented to solve a general system of variational inequalities with the hierarchical
variational inequality constraint for an infinite family of nonexpansive mappings. Strong convergence theorems are given in
a uniformly convex and 2-uniformly smooth Banach space. The results improve and extend the corresponding results in the
earlier and recent literature.
3136
3154
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities
China
zenglc@hotmail.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, and Research Center of Nonlinear Analysis and Optimization
Department of Medical Research
Kaohsiung Medical University
Kaohsiung Medical University Hospital
Taiwan
Taiwan
simplex_liou@hotmail.com
Ching-Fen
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Variational inequalities
nonexpansive mapping
fixed point
implicit iterative algorithm.
Article.28.pdf
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]
Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators
Hardy type estimates for commutators of fractional integrals associated with Schrodinger operators
en
en
We consider the Schrödinger operator \(L = -\Delta + V\) on \(\mathbb{R}^n\), where \(n \geq 3\) and the nonnegative potential \(V\) belongs to
reverse Hölder class \(RH_{q1}\) for some \(q_1 > n/2\) . Let \(I_\alpha\) be the fractional integral associated with \(L\), and let \(b\) belong to a new
Campanato space \(\Lambda_\beta^\theta(\rho)\). In this paper, we establish the boundedness of the commutators \([b, I_\alpha]\) from \(L^p(R^n)\) to \(L^q(R^n)\)
whenever \(1/q=1/p-(\alpha+\beta)/n, 1<p<n/(\alpha+\beta)\). When \(\frac{n}{n+\beta}<p\leq 1,1/q=1/p-(\alpha+\beta)/n\), we show that \([b, I_\alpha]\) is
bounded from \(H^p_
L(R^n)\) to \(L^q(R^n)\). Moreover, we also prove that \([b, I_\alpha]\) maps \(H_L^{\frac{n}{n+\beta}}(R^n)\) continuously into weak \(L^{\frac{n}{n-\alpha}}(R^n)\).
3155
3167
Yinhong
Xia
School of Mathematics and Statistics
Huanghuai University
P. R. China
xiayh03@163.com
Min
Chen
School of Mathematics and Statistics
Huanghuai University
P. R. China
chenmin2002@yeah.net
Schrödinger operator
commutator
Campanato space
fractional integral
Hardy space.
Article.29.pdf
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]
Fixed point approximation of multivalued \(\rho\)-quasi-nonexpansive mappings in modular function spaces
Fixed point approximation of multivalued \(\rho\)-quasi-nonexpansive mappings in modular function spaces
en
en
The purpose of this paper is to investigate some convergence theorems in fixed point theory for \(\rho\)-quasi-nonexpansive
multivalued mappings in modular function spaces using a faster iterative process. Examples are provided to validate our
results.
3168
3179
Safeer Hussain
Khan
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
safeer@qu.edu.qa;safeerhussain5@yahoo.com
Mujahid
Abbas
Department of Mathematics
Department of Mathematics
GC University
King Abdulaziz University
Pakistan
Saudi Arabia
abbas.mujahid@gmail.com
Sartaj
Ali
Department of Mathematics
Women University of Azad Jammu and Kashmir
Pakistan
sartajali2004@yahoo.com
Fixed point
multivalued \(\rho\)-quasi-nonexpansive mapping
iterative process
modular function space.
Article.30.pdf
[
[1]
M. Abbas, T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik, 66 (2014), 223-234
##[2]
T. D. Benavides, M. A. Khamsi, S. Samadi, Asymptotically regular mappings in modular function spaces, Sci. Math. Jpn., 53 (2001), 295-304
##[3]
B. A. B. Dehaish, W. M. Kozlowski, Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in modular function spaces, Fixed Point Theory Appl., 2012 (2012), 1-23
##[4]
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##[5]
M. A. Khamsi, W. M. Kozolowski, Fixed Point Theory in Modular Function Spaces, Springer, Berlin (2015)
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S. H. Khan, M. Abbas, Approximating fixed points of multivalued \(\rho\)-nonexpansive mappings in modular function spaces, Fixed Point Theory Appl., 2014 (2014), 1-9
##[7]
S. H. Khan, M. Abbas, S. Ali, Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process, Acta Math. Sin. (Engl. Ser.), 30 (2014), 1231-1241
##[8]
A. Razani, V. Rakocevic, Z. Goodarzi, Non-self mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math., 8 (2010), 357-366
]
Common fixed point theorems for Ćirić type mappings in b-metric spaces without any completeness assumption
Common fixed point theorems for Ćirić type mappings in b-metric spaces without any completeness assumption
en
en
In this paper, we establish some common fixed point theorems for four mappings satisfying Ćirić type contractive condition
in b-metric spaces without any completeness assumption. Our results improve and generalize the results in the very recent
papers ([Z.-Z. Yang, H. Sadati, S. Sedghi, N. Shobe, J. Nonlinear Sci. Appl., 8 (2015), 1022–1031], [V. Ozturk, S. Radenović,
SpringerPlus, 5 (2016), 10 pages]). Particularly, the contractive constant \(\frac{k}{b^2}\) in the result of Yang et al. is enlarged to \(\frac{k}{b}\)
. Some
examples are provided to support our results.
3180
3190
Borimandafu
Wu
School of Mathematical Sciences
Inner Mongolia University
China
Fei
He
School of Mathematical Sciences
Inner Mongolia University
China
hefei@imu.edu.cn
Tao
Xu
School of Mathematical Sciences
Inner Mongolia University
China
Common fixed point
Ćirić type contractive mapping
(CLRS)-property
b-metric space.
Article.31.pdf
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M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188
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J. Ali, M. Imdad, D. Bahuguna, Common fixed point theorems in Menger spaces with common property (E.A), Comput. Math. Appl., 60 (2010), 3152-3159
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H. Aydi, S. Chauhan, S. Radenović, Fixed points of weakly compatible mappings in G-metric spaces satisfying common limit range property, Facta Univ. Ser. Math. Inform., 28 (2013), 197-210
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H. Aydi, E. Karapınar, B. Samet, Fixed points for generalized (\(\alpha,\psi\))-contractions on generalized metric spaces, J. Inequal. Appl., 2014 (2014), 1-16
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H. Aydi, C. Vetro, W. Sintunavarat, P. Kumam, Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-18
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G. V. R. Babu, P. D. Sailaja, Common fixed points of ( \(\psi,\phi\))-weak quasi contractions with property (E.A.), Int. J. Math. Sci. Comput., 1 (2011), 29-37
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S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
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C. Di Bari, P. Vetro, Nonlinear quasi-contractions of Ćirić type, Fixed Point Theory, 13 (2012), 453-459
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W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261
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F. He, X.-Y. Nan, A unified view on common fixed point theorems for Ćirić quasi-contraction maps, Fixed Point Theory Appl., 2015 (2015), 1-17
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M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 1-15
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H. K. Nashine, Z. Kadelburg, Cyclic generalized \(\varphi\)-contractions in b-metric spaces and an application to integral equations, Filomat, 28 (2014), 2047-2057
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H. K. Nashine, B. Samet, C. Vetro, Fixed point theorems in partially ordered metric spaces and existence results for integral equations, Numer. Funct. Anal. Optim., 33 (2012), 1304-1320
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T. Nazir, M. Abbas, Common fixed points of two pairs of mappings satisfying (E.A)-property in partial metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
##[20]
V. Ozturk, S. Radenović, Some remarks on b-(E.A)-property in b-metric spaces, SpringerPlus, 5 (2016), 1-10
##[21]
V. Ozturk, D. Turkoglu, Common fixed point theorems for mappings satisfying (E.A)-property in b-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 1127-1133
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A. F. Roldán-López-de-Hierro, E. Karapınar, H. H. Alsulami, A short-note on ‘Common fixed point theorems for noncompatible self-maps in generalized metric spaces, J. Inequal. Appl., 2015 (2015), 1-14
##[23]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 1-14
##[24]
Z.-Z. Yang, Common fixed point theorems for non-compatible self-maps in generalized metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
##[25]
Z.-Z. Yang, H. Sadati, S. Sedghi, N. Shobe, Common fixed point theorems for non-compatible self-maps in b-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 1022-1031
]
Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators
Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators
en
en
A mathematical system of equations using the concept of fractional differentiation with non-local and non-singular kernel
has been analysed in this work. The developed mathematical model is designed to portray the spread of Zika virus within a
given population. We presented the equilibrium point and also the reproductive number. The model was solving analytically
using the Adams type predictor-corrector rule for Atangana-Baleanu fractional integral. The existence and uniqueness exact
solution was presented under some conditions. The numerical replications were also presented.
3191
3200
Badr Saad T.
Alkahtani
Department of mathematics, colle of science
King Saud University
Saudi Arabia
balqahtani1@ksu.edu.sa
Abdon
Atangana
Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
abdonatangana@yahoo.fr
Ilknur
Koca
Department of Mathematics, Faculty of Sciences
Mehmet Akif Ersoy University
Turkey
ikoca@mehmetakif.edu.tr
Zika virus
reproduction number
numerical approximation.
Article.32.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]
B. S. T. Alkahtani, Chua’s circuit model with Atangana-Baleanu derivative with fractional order, Chaos Solitons Fractals, 89 (2016), 547-551
##[3]
A. Atangana, D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769
##[4]
A. Atangana, D. Baleanu, Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer, J. Eng. Mech., 143 (2017), 4016005-01
##[5]
A. Atangana, I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016), 447-454
##[6]
E. Bonyah, K. O. Okosun, Mathematical modeling of Zika virus, Asian Pac. J. Trop. Dis., 6 (2016), 673-679
##[7]
L.-P. Chen, J.-F. Qu, Y. Chai, R.-C. Wu, G.-Y. Qi, Synchronization of a class of fractional-order chaotic neural networks, Entropy, 15 (2013), 3265-3276
##[8]
J. Hadamard, Essai sur l’étude des fonctions données par leur développement de Taylor, J. Mat. Pure Appl. Ser., 4 (1892), 101-186
##[9]
U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218 (2011), 860-865
##[10]
J. Lessler, L. H. Chaisson, L. M. Kucirka, Q.-F. Bi, K. Grantz, H. Salje, A. C. Carcelen, C. T. Ott, J. S. Sheffield, N. M. Ferguson, D. A. Cummings, Assessing the global threat from Zika virus, Science, 353 (2016), 663-673
##[11]
F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fract. Calc. Appl. Anal., 4 (2001), 153-192
##[12]
O. O. Makinde, K. O. Okosun, Impact of chemo-therapy on optimal control of malaria disease with infected immigrants, Biosyst, 104 (2011), 32-41
##[13]
O. O. Makinde, K. O. Okosun, Modelling the impact of drug resistance in malaria transmission and its optimal control analysis, Int. J. Phys. Sci., 6 (2011), 6479-6487
]
Common tripled fixed point theorem in two rectangular b-metric spaces and applications
Common tripled fixed point theorem in two rectangular b-metric spaces and applications
en
en
In this paper, we establish some new common tripled fixed point theorems for mappings defined on a set equipped with
two rectangular b-metrics. We also provide illustrative examples in support of our new results. In the end of the paper, we
give an existence and uniqueness theorem for a class of nonlinear integral equations by using the obtained result. The results
presented in this paper generalize the well-known comparable results in the literature.
3201
3216
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
mathgufeng@163.com
Liya
Liu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
846883245@qq.com
Rectangular b-metric space
contractive mappings
tripled coincidence point
common tripled fixed point
\(\omega\)-compatible mapping pairs.
Article.33.pdf
[
[1]
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
##[2]
J. Ahmad, M. Arshad, C. Vetro, On a theorem of Khan in a generalized metric space, Int. J. Anal., 2013 (2013), 1-6
##[3]
M. Arshad, J. Ahmad, E. Karapınar, Some common fixed point results in rectangular metric spaces, Int. J. Anal., 2013 (2013), 1-7
##[4]
H. Aydi, M. Abbas, W. Sintunavarat, P. Kumam, Tripled fixed point of W-compatible mappings in abstract metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-20
##[5]
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
##[6]
H. Aydi, E. Karapınar, H. Lakzian, Fixed point results on a class of generalized metric spaces, Math. Sci. (Springer), 2012 (2012), 1-6
##[7]
N. Bilgili, E. Karapınar, D. Turkoglu, A note on common fixed points for (\(\psi,\alpha,\beta\))-weakly contractive mappings in generalized metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-6
##[8]
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37
##[9]
N. Cakić, Coincidence and common fixed point theorems for (\(\psi,\phi\)) weakly contractive mappings in generalized metric spaces, Filomat, 27 (2013), 1415-1423
##[10]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[11]
P. Das, L. K. Dey, Fixed point of contractive mappings in generalized metric spaces, Math. Slovaca, 59 (2009), 499-504
##[12]
C. Di Bari, P. Vetro, Common fixed points in generalized metric spaces, Appl. Math. Comput., 218 (2012), 7322-7325
##[13]
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
##[14]
H.-S. Ding, V. Ozturk, S. Radenović, On some new fixed point results in b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 378-386
##[15]
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
##[16]
A. Flora, A. Bellour, A. Al-Bsoul, Some results in fixed point theory concerning generalized metric spaces, Mat. Vesnik, 61 (2009), 203-208
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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
##[19]
H. Işik, 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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Split equality problem with equilibrium problem, variational inequality problem, and fixed point problem of nonexpansive semigroups
Split equality problem with equilibrium problem, variational inequality problem, and fixed point problem of nonexpansive semigroups
en
en
In this paper, we present a new algorithm for the split equality problem for finding a common element of solution of
equilibrium problem, solution of variational inequality problem for monotone and Lipschitz continuous operators, and common
fixed point of nonexpansive semigroups. We establish strong convergence of the algorithm in an infinite dimensional Hilbert
spaces. Our results improve and generalize some recent results in the literature.
3217
3230
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Mohammad
Eslamian
Department of Mathematics
University of Science and Technology of Mazandaran
Iran
mhmdeslamian@gmail.com
Split equality problem
equilibrium problem
variational inequality
nonexpansive semigroups
fixed point.
Article.34.pdf
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]
Generalization and reverses of the left Fejer inequality for convex functions
Generalization and reverses of the left Fejer inequality for convex functions
en
en
In this paper we establish a generalization of the left Fej´er inequality for general Lebesgue integral on measurable spaces
as well as various upper bounds for the difference
\[\frac{1}{\int^b_a g(x)dx} \int^b_ah(x)g(x)dx-h\left(\frac{a+b}{2}\right),\]
where \(h : [a, b] \rightarrow \mathbb{R}\) is a convex function and \(g : [a, b] \rightarrow [0,\infty)\) is an integrable weight. Applications for discrete means and
Hermite-Hadamard type inequalities are also provided.
3231
3244
S. S.
Dragomir
Mathematics, School of Engineering & Science
chool of Computational & Applied Mathematics
Victoria University
University of the Witwatersrand
Australia
South Africa
sever.dragomir@vu.edu.au
Convex functions
integral inequalities
Jensen’s type inequalities
Fejér type inequalities
Lebesgue integral
Hermite-Hadamard type inequalities
special means.
Article.35.pdf
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]
Permanence of a stochastic delay competition model with Lévy jumps
Permanence of a stochastic delay competition model with Lévy jumps
en
en
Permanence is one of the most important topics in biomathematics. The question of permanence of stochastic multi-species
models is challenging because the current approaches can not be used. In this paper, an asymptotic approach is used, and
sufficient criteria for permanence of a general n-species stochastic delay Lotka-Volterra competition model with Lévy jumps are
established. It is also shown that these criteria are sharp in some cases. The results reveal that the stochastic noises play a key
role in the permanence. This approach can be also applied to investigate the permanence of other stochastic population models
with/without time delay and/or Lévy noises.
3245
3260
Meng
Liu
School of Mathematical Science
School of Mathematics and Statistics
Huaiyin Normal University
Northeast Normal University
P. R. China
P. R. China
liumeng0557@sina.com
Meiling
Deng
School of Mathematical Science
Huaiyin Normal University
P. R. China
Zhaojuan
Wang
School of Mathematical Science
Huaiyin Normal University
P. R. China
Permanence
stochastic perturbations
delay.
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S. J. Schreiber, M. Benaïm, K. A. S. Atchadé, Persistence in fluctuating environments, J. Math. Biol., 62 (2011), 655-683
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H. L. Smith, H. R. Thieme, Dynamical systems and population persistence, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2011)
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K. Tran, G. Yin, Stochastic competitive Lotka-Volterra ecosystems under partial observation: feedback controls for permanence and extinction, J. Franklin Inst., 351 (2014), 4039-4064
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M. Vasilova, M. Jovanović, Stochastic Gilpin-Ayala competition model with infinite delay, Appl. Math. Comput., 217 (2011), 4944-4959
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]
Strong duality with super efficiency in set-valued optimization
Strong duality with super efficiency in set-valued optimization
en
en
This paper is devoted to the study of four dual problems of a primal vector optimization problem involving nearly subconvexlike
set-valued mappings. For each dual problem, a strong duality theorem with super efficiency is established. The strong
duality result can be expressed as follows: starting from a super minimizer of the primal problem, a super maximizer of the
dual problem can be constructed such that the corresponding objective values of both problems are equal. The results improve
the corresponding ones in the literature.
3261
3272
Guolin
Yu
Institute of Applied Mathematics
North Minzu University
P. R. China
guolin_yu@126.com
Super efficiency
Henig proper efficiency
nearly subconvexlike set-valued mappings
set-valued optimization
strong duality.
Article.37.pdf
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T. Q. Bao, B. S. Mordukhovich, Necessary conditions for super minimizers in constrained multiobjective optimization, J. Global Optim., 43 (2009), 533-552
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]
Persistence and non-persistence of a stochastic food chain model with finite delay
Persistence and non-persistence of a stochastic food chain model with finite delay
en
en
In this paper, we study a three species predator-prey time-delay chain model with stochastic perturbation. First, we analyze
that this system has a unique positive solution. Then, we deduce the conditions that the system is persistent in time average.
After that, conditions for the system going to be extinction in probability are established. At last, numerical simulations are
carried out to support our results.
3273
3287
Haihong
Li
Department of Basic Science
Jilin Construction University
China
lihaihong888999@126.com
Haixia
Li
School of Business
Changchun Guanghua University
China
Fuzhong
Cong
Department of Basic Courses
Air Force Aviation University
China
Stochastic differential equation
persistent
non-persistent
extinction.
Article.38.pdf
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Linking of Bernstein-Chlodowsky and Szász-Appell-Kantorovich type operators
Linking of Bernstein-Chlodowsky and Szász-Appell-Kantorovich type operators
en
en
In the present paper, we define a sequence of bivariate operators by linking the Bernstein-Chlodowsky operators and the
Szász-Kantorovich operators based on Appell polynomials. First, we establish the moments of the operators and then determine
the rate of convergence of these operators in terms of the total and partial modulus of continuity. Next, we obtain the order
of approximation of the considered operators in a weighted space. Furthermore, we define the associated GBS (Generalized
Boolean Sum) operators of the linking operators and then study the rate of convergence with the aid of the Lipschitz class of
Bögel continuous functions and the mixed modulus of smoothness.
3288
3302
P. N.
Agrawal
Department of Mathematics
Indian Institute of Technology Roorkee
India
pnappfma@gmail.com
D.
Kumar
Department of Mathematics
Indian Institute of Technology Roorkee
India
dharmendrak.dav@gmail.com
S.
Araci
Department of Economics, Faculty of Economics, Administrative and Social Sciences
Hasan Kalyoncu University
Turkey
mtsrkn@hotmail.com
Appell polynomials
weighted approximation
GBS operators
partial and mixed modulus of smoothness
Peetre’s K-functional.
Article.39.pdf
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[1]
P. N. Agrawal, N. Ispir, Degree of approximation for bivariate Chlodowsky-Szász-Charlier type operators, Results Math., 69 (2016), 369-385
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]
On the dynamics of a five-order fuzzy difference equation
On the dynamics of a five-order fuzzy difference equation
en
en
Our aim in this paper is to investigate the existence and uniqueness of the positive solutions and the asymptotic behavior
of the equilibrium points of the fuzzy difference equation
\[x_{n+1}=\frac{Ax_{n-1}x_{n-2}}{D+Bx_{n-3}+Cx_{n-4}}, n=0,1,2,...,\]
where \(x_n\) is a sequence of positive fuzzy numbers, the parameters \(A, B, C, D\) and the initial conditions \(x_{-4}, x_{-3}, x_{-2}, x_{-1}, x_0\)
are positive fuzzy numbers. Moreover, some numerical examples to the difference system are given to verify our theoretical
results.
3303
3319
Changyou
Wang
College of Science
School of Applied Mathematics
Chongqing University of Posts and Telecommunications
Chengdu University of Information Technology
P. R. China
P. R. China
Xiaolin
Su
College of Science
Chongqing University of Posts and Telecommunications
P. R. China
Ping
Liu
College of Science
Chongqing University of Posts and Telecommunications
P. R. China
Xiaohong
Hu
College of Science
Chongqing University of Posts and Telecommunications
P. R. China
huxh@cqupt.edu.cn
Rui
Li
College of Automation
Chongqing University of Posts and Telecommunications
P. R. China
liruimath@qq.com
Fuzzy difference equation
existence
uniqueness
equilibrium point
asymptotic behavior.
Article.40.pdf
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]
Design of hybrid controller for synchronization control of Chen chaotic system
Design of hybrid controller for synchronization control of Chen chaotic system
en
en
This paper deals with the synchronization control of Chen chaotic system using a hybrid control which includes continuous
state feedback control, the impulsive control and the nonlinear feedback law. To this end, a hybrid controller based on linear
matrix inequality (LMI) and average dwell time (ADT) is derived by employing impulsive control theory. The main advantage
of the result lies in that, for one thing, they are complementary to each other, that is, when the impulse inputs occur in terms of
disturbances which do harm to the synchronization, the continuous state feedback control will cover the weakness and stabilize
the error system, and conversely, when the continuous state feedback control is given in terms of external disturbances which
do harm to the synchronization, the impulsive control input will stabilize the error system; for another, the developed result
is based on ADT condition and dropped the restriction on the upper and lower bounds of the impulsive intervals. Finally,
numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.
3320
3327
Xiaoyu
Zhang
School of Mathematics and Statistics
Shandong Normal University
P. R. China
Xiaodi
Li
School of Mathematics and Statistics
Institute of Data Science and Technology
Shandong Normal University
Shandong Normal University
P. R. China
P. R. China
Xiuping
Han
School of Mathematics and Statistics
Shandong Normal University
P. R. China
lxd@sdnu.edu.cn
Chen system
impulsive control
synchronization
average dwell-time (ADT)
hybrid controller.
Article.41.pdf
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]
An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation
An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation
en
en
An integrable coupling hierarchy of Dirac integrable hierarchy is presented by means of zero curvature representation.
A Hamiltonian operator involving two parameters is introduced, and it is used to derive a pair of Hamiltonian operators.
A bi-Hamiltonian structure of the obtained integrable coupling hierarchy is constructed with the aid of Magri pattern of bi-
Hamiltonian formulation. Moreover, we prove the Liouville integrability of the obtained integrable coupling hierarchy and
establish a Darboux transformation of the integrable coupling. As an application, an exact solution of the integrable coupling of
Dirac equation is given.
3328
3343
Xi-Xiang
Xu
College of Mathematics and Systems Science
Shandong University of Science and Technology
China
xixiang-xu@sohu.com
Ye-Peng
Sun
School of Mathematics and Quantitative Economics
Shandong University of Finance and Economics
China
Dirac integrable hierarchy
integrable coupling
Hamiltonian operator
Magri pattern
bi-Hamiltonian structure
Darboux transformation.
Article.42.pdf
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Common fixed point for fuzzy mappings satisfying an implicit \(\varphi\)-contractive conditions in complete metric spaces
Common fixed point for fuzzy mappings satisfying an implicit \(\varphi\)-contractive conditions in complete metric spaces
en
en
In this paper, by using \(F_\varphi\)-type real functions, some common fixed point for fuzzy mappings satisfying an implicit \(\varphi\)-
contractive conditions in complete metric spaces are established. Our results extend, generalize, and improve some existing
results. Moreover, some applications and two examples are given here to illustrate the validity of the hypotheses of our main
results.
3344
3356
Ming-Liang
Song
Mathematics and Information Technology School
Jiangsu Second Normal University
P. R. China
mlsong2004@163.com
Common fixed point
fuzzy mapping
implicit \(\varphi\)-contractive condition
multi-valued mappings
complete metric space.
Article.43.pdf
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]
Lyapunov inequality for a class of fractional differential equations with Dirichlet boundary conditions
Lyapunov inequality for a class of fractional differential equations with Dirichlet boundary conditions
en
en
In this paper we present Lyapunov inequality for the following fractional boundary value problem
\[
\begin{cases}
\frac{d}{dt}(\frac{1}{2} _aD_t^{-\beta}u'(t)+\frac{1}{2} _tD_b^{-\beta}u'(t))+\omega(t)u(t)=0,\,\,\,\,\, \quad a<t<b,\\
u(a)=u(b)=0.
\end{cases}
\]
where \( _aD_t^{-\beta}\) and \( _tD_b^{-\beta}\) are the left and right Riemann-Liouville fractional integrals of order \(0\leq\beta<1\), respectively, and
\(\omega\in L^1([a,b],\mathbb{R})\). Using the obtained inequality, we provide lower bounds for the first eigenvalue of the fractional differential
equations with homogeneous Dirichlet boundary problem.
3357
3363
Yasong
Chen
Department of Mathematics
Tianjin Polytechnic University
China
yasongchen@126.com
Yeong-Cheng
Liou
Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics & 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
Ching-Hua
Lo
Department of Management
Yango University
China
bde_lo@sina.com
Lyapunov type inequality
fractional differential equations
boundary value problem
eigenvalue.
Article.44.pdf
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]