]>
2016
9
2
ISSN 2008-1898
366
A study of some properties of an n-order functional inclusion
A study of some properties of an n-order functional inclusion
en
en
The purpose of this paper is to study the solution set of the functional inclusion of n-th order of the following
form:
\[x(t) \in G(t; x(f_1(t)); ...; x(f_n(t))); t \in X;\quad (1)\]
where the function \(G: X\times Y^n\rightarrow P_{cl,cv}(Y)\) and \(f_1; f_2; ...; f_n : X \rightarrow X\) are given. The approach is based
on some fixed point theorems for multivalued operators, satisfying the nonlinear contraction condition, see
[V. L. Lazăr, Fixed Point Theory Appl., 2011 (2011), 12 pages].
350
356
Tania Angelica
Lazăr
Department of Mathematics
Technical University of Cluj-Napoca
Romania
tanialazar@mail.utcluj.ro
Vasile Lucian
Lazăr
The Faculty of Economics
Western University of Arad
Romania
vasilazar@yahoo.com
Functional inclusion
multivalued weakly Picard operator
fixed point
\(\varphi\)-contraction
data dependence
well-posedness
Ulam-Hyers stability.
Article.1.pdf
[
[1]
V. L. Lazăr, Fixed point theory for multivalued \(\varphi\)-contractions , Fixed Point Theory Appl., 2011 (2011), 1-12
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I. R. Petre, Fixed point theorems in E-b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 264-271
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A. Petruşel , Operatorial Inclusions, House of the Book of Science, Cluj-Napoca (2002)
##[4]
A. Petruşel , Multivalued weakly Picard operators and applications, Scientiae Math. Jpn., 59 (2004), 167-202
##[5]
A. Petruşel, I. A. Rus , Multivalued Picard and weakly Picard operators, International Conference on Fixed Point Theory and Applications, Yokohama Publ., Yokohama, (2004), 207-226
##[6]
A. Petruşel, I. A. Rus, The theory of a metric fixed point theorem for multivalued operators, In: L.J. Lin, A. Petruşel, H.K. Xu, Fixed Point Theory and its Applications, Yokohama Publ., (2010), 161-175
##[7]
A. Petruşel, I. A. Rus, J. C. Yao , Well-posedness in the generalized sense of the fixed point problems, Taiwan. J. Math., 11 (2007), 903-914
##[8]
R. Węgrzyk , Fixed point theorems for multivalued functions and their applications to functional equations , Dissertationes Math. (Rozprawy Mat.), 201 (1982), 1-28
]
Unbounded solutions of second order discrete BVPs on infinite intervals
Unbounded solutions of second order discrete BVPs on infinite intervals
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en
In this paper, we study Sturm-Liouville boundary value problems for second order difference equations on a
half line. By using the discrete upper and lower solutions, the Schäuder fixed point theorem, and the degree
theory, the existence of one and three solutions are investigated. An interesting feature of our existence
theory is that the solutions may be unbounded.
357
369
Hairong
Lian
School of Science
China University of Geosciences
P. R. China
lianhr@cugb.edu.cn
Jingwu
Li
School of Science
China University of Geosciences
P. R. China
Ravi P
Agarwal
Department of Mathematics
Texas A&M University-Kingsville
USA
Coincidence point
discrete boundary value problem
infinite interval
upper solution
lower solution
degree theory common fixed point.
Article.2.pdf
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V. S. Ryaben'kiim, S. V. Tsynkov , An effective numerical technique for solving a special class of ordinary difference equations, Appl. Numer. Math., 18 (1995), 489-501
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H. B. Thompson, C. C. Tisdell, Systems of difference equations associated with boundary value problems for second order systems of ordinary differential equations , J. Math. Anal. Appl., 248 (2000), 333-347
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H. B. Thompson, Topological methods for some boundary value problems, Comput. Math. Appl., 42 (2001), 487-495
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]
The solutions of a class of operator equations based on different inequality
The solutions of a class of operator equations based on different inequality
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en
In this paper, by using random fixed point index theory, some new boundary conditions based on strictly
convex or strictly concave functions are established and some new theorems for the solutions of a class
of random semi-closed 1-set-contractive operator equations \(A(\omega; x) = \mu x\) are obtained, which extend and
generalize some corresponding results of Wang [S. Wang, Fixed Point Theory Appl., 2011 (2011), 7 pages].
Finally, an application to a class of random nonlinear integral equations is given to illustrate the usability
of the obtained results.
370
376
Xiaofang
Yan
Department of Mathematics
Nanchang University
P. R. China
xiaoxiaoyan_green@163.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Zhaoqi
Wu
Department of Mathematics
Nanchang University
P. R. China
wuzhaoqi_conquer@163.com
Real Banach space
random semi-closed 1-set-contractive operator
random topological degree.
Article.3.pdf
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]
Some base spaces and core theorems of new type
Some base spaces and core theorems of new type
en
en
In this paper, we constructed two new base sequence spaces, denoted \(rf\) and \(rf_0\), and we investigated some
of their important properties. Then, by using matrix domains, we defined other sequence spaces on these
base spaces, called \(zrf\) and \(zrf_0\). Finally, we introduced the \(B_\hat{R}\) core of a complex-valued sequence and we
examined some inclusion theorems related to this new type of core.
377
391
Zarife
Zararsiz
Science and Art Faculty
Nevşehir Hacı Bektaş Veli University
Turkey
zarifezararsiz@nevsehir.edu.tr
Mehmet
Şengönül
Science and Art Faculty
Nevşehir Hacı Bektaş Veli University
Turkey
msengonul@nevsehir.edu.tr
Kuddusi
Kayaduman
Science and Art Faculty
G. Antep University
Turkey
kayaduman@gantep.edu.tr
Almost convergence
base space
isomorphism
dual
matrix transformation
core theorem
Article.4.pdf
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]
A proximal splitting method for separable convex programming and its application to compressive sensing
A proximal splitting method for separable convex programming and its application to compressive sensing
en
en
Recently, by taking full exploitation to the special structure of the separable convex programming, some
splitting methods have been developed. However, in some practical applications, these methods need to
compute the inverse of a matrix, which maybe slow down their convergence rate, especially when the
dimension of the matrix is large. To solve this issue, in this paper we shall study the Peaceman-Rachford
splitting method (PRSM) by adding a proximal term to its first subproblem and get a new method named
proximal Peaceman-Rachford splitting method (PPRSM). Under mild conditions, the global convergence of
the PPRSM is established. Finally, the effeciency of the PPRSM is illustrated by testing some applications
arising in compressive sensing.
392
403
Hongchun
Sun
School of Sciences
Linyi University
P. R. China
sunhc68@126.com
Min
Sun
School of Mathematics and Statistics
Zaozhuang University
P. R. China
ziyouxiaodou@163.com
Houchun
Zhou
School of Sciences
Linyi University
P. R. China
zhouhouchun@163.com
Proximal Peaceman-Rachford splitting method
separable convex programming
compressive sensing.
Article.5.pdf
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D. R. Han, X. M. Yuan, Convergence analysis of the Peaceman-Rachford splitting method for nonsmooth convex optimization, J. Optim. Theory Appl., (Under-revision)
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B. He, H. Liu, Z. Wang, X. Yuan , A strictly contractive Peaceman-Rachford splitting method for convex programming , SIAM J. Optim., 24 (2014), 1011-1040
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]
Chaos in nonautonomous discrete fuzzy dynamical systems
Chaos in nonautonomous discrete fuzzy dynamical systems
en
en
This paper is devoted to a study of relations between chaotic properties of nonautonomous dynamical system
and its induced fuzzy system. More specially, we study transitivity, periodic density and sensitivity in an
original nonautonomous system and its connections with the same ones in its fuzzified system.
404
412
Yaoyao
Lan
Department of Mathematics and Finance
Key Laboratory
Chongqing University of Arts and Sciences
Chongqing University of Arts and Sciences
China
China
yylanmath@163.com
Discrete dynamical system
nonautonomous
fuzzy
chaos.
Article.6.pdf
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]
Superstability of Pexiderized functional equations arising from distance measures
Superstability of Pexiderized functional equations arising from distance measures
en
en
In this paper, we obtain the superstability of the functional equation
\(f(pr; qs) + g(ps; qr) = \theta(pq; rs)h(p; q)k(r; s)\)
for all \(p; q; r; s \in G\), where \(G\) is an Abelian group, \(f; g; h; k\) are functionals on \(G^2\), and \(\theta\) is a cocycle on \(G^2\).
This functional equation is a generalized form of the functional equation \(f(pr; qs)+f(ps; qr) = f(p; q) f(r; s)\),
which arises in the characterization of symmetrically compositive sum-form distance measures and the information measures, and also they can be represented as products of some multiplicative functions and the
exponential functional equations. As corollaries, we obtain the superstability of the many functional equations (combination of three variables functions, for example: \(f(pr; qs) + g(ps; qr) = \theta(pq; rs)h(p; q)g(r; s))\).
413
423
Gwang Hui
Kim
Department of Applied Mathematics
Kangnam University
Korea
ghkim@kangnam.ac.kr
Young Whan
Lee
Department of Computer Hacking and Information Security, College of Natural Science
Daejeon University
Republic of Korea
ywlee@dju.ac.kr
Distance measure
superstability
multiplicative function
stability of functional equation.
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A novel double integral transform and its applications
A novel double integral transform and its applications
en
en
We introduce a new double integral equation and prove some related theorems. We then present some
useful tools for the new integral operator, and use this operator to solve partial differential equations with
singularities of a given type.
424
434
Abdon
Atangana
Institute for Groundwater Studies, Faculty of Natural and Agricultural Science
University of the Free State, ,
South Africa
abdonatangana@yahoo.fr
Badr Saad T.
Alkahtani
Department of Mathematics, College of Science
King Saud University
Saudi Arabia
balqahtani1@ksu.edu.sa
Coincidence point
new double integral transform
Laplace transform
second order partial differential equation.
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Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter
Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter
en
en
Let \(L\) denote the operator generated in\(L_2(\mathbb{R}_+;E)\) by the differential expression
\[l(y) = -y'' + Q(x)y; \qquad x \in \mathbb{R}_+\];
and the boundary condition \((A_0 + A_1\lambda)Y' (0; \lambda) - (B_0 + B_1\lambda)Y (0; \lambda) = 0\) , where \(Q\) is a matrix-valued
function and \(A_0; A_1; B_0; B_1\) are non-singular matrices, with \(A_0B_1 - A_1B_0 \neq 0\): In this paper, using the
uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of
\(L\). In particular, we obtain the conditions on q under which the operator \(L\) has a finite number of the
eigenvalues and the spectral singularities.
435
442
Deniz
Katar
Faculty of Sciences, Department of Mathematics
Ankara University
Turkey
deniz.ktr@hotmail.com
Murat
Olgun
Faculty of Sciences, Department of Mathematics
Ankara University
Turkey
olgun@ankara.edu.tr
Cafer
Coskun
Faculty of Sciences, Department of Mathematics
Ankara University
Turkey
ccoskun@ankara.edu.tr
Eigenvalues
spectral singularities
spectral analysis
Sturm-Liouville operator
non-selfadjoint matrix operator
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]
Symmetric identities of higher-order degenerate q-Euler polynomials
Symmetric identities of higher-order degenerate q-Euler polynomials
en
en
In this paper, we study the higher-order degenerate \(q\)-Euler polynomials and give some identities of symmetry
on these polynomials derived from symmetric properties for certain multivariate fermionic \(p\)-adic \(q\)-integrals
on \(\mathbb{Z}_p\).
443
451
Dae San
Kim
Department of Mathematics
Sogang University, , .
Republic of Korea
dskim@sogang.ac.kr
Taekyun
Kim
Department of Mathematics
Kwangwoon University
Republic of Korea
tkkim@kw.ac.kr
Symmetry
identity
higher-order degenerate q-Euler polynomial.
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]
Anti-periodic BVP for Volterra integro-differential equation of fractional order \(1<\alpha \leq 2\), involving Mittag-Leffler function in the kernel
Anti-periodic BVP for Volterra integro-differential equation of fractional order \(1<\alpha \leq 2\), involving Mittag-Leffler function in the kernel
en
en
In this paper, we consider an anti-periodic Boundary Value Problem for Volterra integro-differential equation
of fractional order \(1<\alpha \leq 2\); with generalized Mittag-Leffler function in the kernel. Some existence and
uniqueness results are obtained by using some well known fixed point theorems. We give some examples to
exhibit our results.
452
460
Hüseyin
Aktuğlu
Eastern Mediterranean University
Turkey
huseyin.aktuglu@emu.edu.tr
Mehmet Ali
Özarslan
Eastern Mediterranean University
Turkey
mehmetali.ozarslan@emu.edu.tr
Fractional derivative
fractional integral
Caputo fractional derivative
boundary value problem
Caputo fractional boundary value problem
integral operators
Mittag-Leffler functions.
Article.11.pdf
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[1]
T. Abdeljawad, D. Baleanu, Caputa q-fractional initial value problems and a q-analogue Mittag-Leffler function, Commun. Nonlinear Sci. Numer. Simulat., 16 (2011), 4682-4688
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R. P. Agarwal, B. Ahmad , Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions, Comput. Math. Appl., 62 (2011), 1200-1214
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P. Agarwal, J. Choi, R. B. Paris, Extended Riemann-Liouville fractional derivative operator and its applications, J. Nonlinear Sci. Appl., 8 (2015), 451-466
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R. P. Agarwal, G. Wang, A. Hobiny, L. Zhang, B. Ahmad, Existence and nonexistence of solutions for nonlinear second order q-integro-difference equations with non-separated boundary conditions, J. Nonlinear Sci. Appl., 8 (2015), 976-985
##[6]
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B. Ahmad, J. J. Nieto, Anti-periodic fractional boundary value problems, Comput. Math. Appl., 62 (2011), 1150-1156
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H. Aktuğlu, M. A. Özarslan , On the solvability of Caputo q-fractional boundary value problem involving p-Laplacian operator, Abstr. Appl. Anal., 2013 (2013), 1-8
##[12]
H. Aktuğlu, M. A. Özarslan, Solvability of differential equations of order \(2 < \alpha <= 3\) involving the p-Laplacian operator with boundary conditions, Adv. Differ. Eqn., 2013 (2013), 1-13
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T. Chen, W. Liu, An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator, Appl. Math. Lett., 25 (2012), 1671-1675
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I. Podlubny, Fractional differential equations, Academy Press, San Diego (1999)
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]
A composition projection method for feasibility problems and applications to equilibrium problems
A composition projection method for feasibility problems and applications to equilibrium problems
en
en
In this article, we propose a composition projection algorithm for solving feasibility problem in Hilbert space.
The convergence of the proposed algorithm are established by using gap vector which does not involve the
nonempty intersection assumption. Moreover, we provide the sufficient and necessary condition for the
convergence of the proposed method. As an application, we investigate the split feasibility equilibrium
problem.
461
470
Jiawei
Chen
School of Mathematics and Statistics
College of Computer Science
Southwest University
Chongqing University
China
China
J.W.Chen713@163.com
Yeong-Cheng
Liou
Department of Information Management
Cheng Shiu University
Taiwan
simplex_liou@hotmail.com
Suhel Ahmad
Khan
Department of Mathematics
BITS-Pilani, Dubai Campus
UAE
khan.math@gmail.com
Zhongping
Wan
School of Mathematics and Statistics
Wuhan University
China
zpwan-whu@126.com
Ching-Feng
Wen
Center for General Education
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
Feasibility problem
gap vector
projection
split feasibility equilibrium problem.
Article.12.pdf
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]
Fixed point theorems for generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings in \(\alpha-\eta-\)complete metric spaces
Fixed point theorems for generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings in \(\alpha-\eta-\)complete metric spaces
en
en
In this paper, we introduce the concept of generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings and prove
the unique fixed point theorems for such mappings in \(\alpha-\eta-\)complete metric spaces without assuming the
subadditivity of \(\psi\). We also give an example for supporting the result and present an application using our
main result to obtain a solution of the integral equation.
471
485
Preeyaluk
Chuadchawna
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
Chuadchawna@hotmail.com
Anchalee
Kaewcharoen
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
anchaleeka@nu.ac.th
Somyot
Plubtieng
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
somyotp@nu.ac.th
\(\alpha-\eta-\)complete metric spaces
\(\alpha-\eta-\)continuous mappings
triangular \(\alpha-\)-orbital admissible mappings
generalized \(\alpha-\eta-\psi-\)Geraghty contraction type mappings.
Article.13.pdf
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S. H. Cho, J. S. Bae, E. Karapinar, Fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
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M. E. Gordji, M. Ramezami, Y. J. Cho, S. Pirbavafa, A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2012 (2012), 1-9
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N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 1-11
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Z. Kadelburg, P. Kumam, S. Radenovi'c, W. Sintunavarat, Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property, Fixed Point Theory Appl., 2015 (2015), 1-14
##[8]
E. Karapinar , \(\alpha-\psi-\)Geraghty contraction type mappings and some related fixed point results, Filomat, 28 (2014), 37-48
##[9]
E. Karapinar, P. Kumam, P. Salimi , On \(\alpha-\psi-\)Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
##[10]
C. Mongkolkeha, Y. J. Cho, P. Kumam, Best proximity points for Geraghty's proximal contraction mappings, Fixed Point Theory Appl., 2013 (2013), 1-17
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O. Popescu, Some new fixed point theorems for \(\alpha-\)Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-12
##[13]
B. Samet, C. Vetro, P. Vetro , Fixed point theorems for \(\alpha-\psi-\)contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
]
A Note on Well-posedness of Nash-type Games Problems with Set Payoff
A Note on Well-posedness of Nash-type Games Problems with Set Payoff
en
en
In this paper, Nash-type games problems with set payoff (for short, NGPSP) are first introduced.
Then, in terms of the measure of noncompactness, some well-posedness results for Nash-type games
problems with set payoff are obtained in Banach spaces.
486
492
Yu
Zhang
College of Statistics and Mathematics
Yunnan University of Finance and Economics
China
zhangyu198606@sina.com
Tao
Chen
College of Public Foundation
Yunnan Open University
China
chentao1cq@126.com
Well-posedness
Nash-type games problems
Hausdorff distance
set payoff.
Article.14.pdf
[
[1]
J. P. Aubin, I. Ekeland , Applied Nonlinear Analysis, Dover Publications, Inc., New York (2006)
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J. W. Chen, Y. J. Cho, X. Q. Ou , Levitin-polyakwell-posedness for set-valued optimization problems with constraints, Filomat, 28 (2014), 1345-1352
##[3]
J. W. Chen, Y. J. Cho, Z. P. Wang, The existence of solutions and well-posedness for bilevel mixed equilibrium problems in Banach spaces, Taiwan. J. Math., 17 (2013), 725-748
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S. J. Li, M. H. Li , Levitin-Polyak well-posedness of vector equilibrium problems, Math. Methods Oper. Res., 69 (2009), 125-140
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W. Y. Zhang, S. J. Li, K. L. Teo, Well-posedness for Set Optimization Problems, Nonlinear Anal., 71 (2009), 3769-3778
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J. Zeng, S. J. Li, W. Y. Zhang, X. W. Xue, Hadamard well-posedness for a set-valued optimization problem, Optim. Lett., 7 (2013), 559-573
]
A fixed point technique for some iterative algorithm with applications to generalized right fractional calculus
A fixed point technique for some iterative algorithm with applications to generalized right fractional calculus
en
en
We present a fixed point technique for some iterative algorithms on a generalized Banach space setting to
approximate a locally unique zero of an operator. Earlier studies such as [I. K. Argyros, Approx. Theory
Appl., 9 (1993), 1{9], [I. K. Argyros, Southwest J. Pure Appl. Math., 1 (1995), 30-36], [I. K. Argyros,
Springer-Verlag Publ., New York, (2008)], [P. W. Meyer, Numer. Funct. Anal. Optim., 9 (1987), 249-259]
require that the operator involved is Fréchet-differentiable. In the present study we assume that the operator
is only continuous. This way we extend the applicability of these methods to include right fractional calculus
as well as problems from other areas. Some applications include fractional calculus involving right generalized
fractional integral and the right Hadamard fractional integral. Fractional calculus is very important for its
applications in many applied sciences.
493
505
George A.
Anastassiou
Department of Mathematical Sciences
University of Memphis
USA
ganastss@memphis.edu
Ioannis K.
Argyros
Department of Mathematical Sciences
Cameron University
USA
iargyros@cameron.edu
Generalized Banach space
fixed point iterative algorithm
semilocal convergence
fixed point right generalized fractional integral.
Article.15.pdf
[
[1]
G. A. Anastassiou, Right general fractional monotone approximation theory, submitted , (2015)
##[2]
G. A. Anastassiou, Univariate right general higher order fractional monotone approximation, submitted , (2015)
##[3]
I. K. Argyros, Newton-like methods in partially ordered linear spaces, Approx. Theory Appl., 9 (1993), 1-9
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I. K. Argyros, Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure, Southwest J. Pure Appl. Math., 1 (1995), 30-36
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I. K. Argyros, Convergence and applications of Newton-type iterations, Springer-Verlag Publ., New York (2008)
##[6]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo , Theory and applications of fractional differential equations, Vol. 2004 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[7]
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]
Asymptotic periodicity for a class of fractional integro--differential equations
Asymptotic periodicity for a class of fractional integro--differential equations
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en
In this paper, we are concerned with the existence and uniqueness of S-asymptotically \(\omega\)-periodic solutions
to a class of fractional integro-differential equations. Some sufficient conditions are established about
the existence and uniqueness of S-asymptotically \(\omega\)-periodic solutions to the fractional integro-differential
equation by applying fixed point theorem combined with sectorial operator, where the nonlinear perturbation
term f is a Lipschitz case and non-Lipschitz case.
506
517
Zhong-Hua
Wu
Basis Course Department
Guangzhou Nanyang Polytechnic
China
w3z3h3@163.com
Fractional integro-differential equation
S-asymptotically \(\omega\)-periodic
fixed point
mild solutions
sectorial operator.
Article.16.pdf
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[1]
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A. Debbouche, J. J. Nieto, Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions, Electron. J. Differential Equations, 2015 (2015), 1-18
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]
On a Family of Surfaces with Common Asymptotic Curve in the Galilean space \(G_3\)
On a Family of Surfaces with Common Asymptotic Curve in the Galilean space \(G_3\)
en
en
In this paper, we obtain the parametric representation for a family of surfaces through a given asymptotic
curve by using the Frenet frame in the Galilean space \(G_3\). Necessary and sufficient conditions are given for
that curve to be an isoasymptotic curve on the parametric surfaces. We also provide an example in support
of our results.
518
523
Zühal Küçükarslan
Yüzbaşı
Faculty of Science, Department of Mathematics
Firat University
Turkey
zuhal2387@yahoo.com.tr
Asymptotic curve
parametric surface
Galilean space.
Article.17.pdf
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E. Bayram, F. Güler, E. Kasap , Parametric representation of a surface pencil with a common asymptotic curve, Comput. Aid. Design, 44 (2012), 637-643
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]
Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate
Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate
en
en
For a viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate
and distributed delays, we analyze the global asymptotic behavior of its solutions. In this model, the rate
of contact between viruses and uninfected target cells and state-dependent removal rate of infected cells
depend on general nonlinear functions. The basic reproduction number for the model is discussed. Under
certain assumptions, it is shown that if \(\Re_0\leq 1\), then the infection-free equilibrium \(P_0\) is globally stable
and the viruses are cleared; If \(\Re_0 > 1\), then there is a unique infection equilibrium, which is globally stable
implying the infection becomes chronic. The global stability results are achieved by appealing to the direct
Lyapunov method.
524
536
Jinliang
Wang
School of Mathematical Science
Heilongjiang University
China
jinliangwang@hlju.edu.cn
Jiying
Lang
School of Mathematical Science
Heilongjiang University
China
jiyinglang@aliyun.com
Feng
Li
School of Science
Linyi University
China
lf0539@126.com
Viral infection model
nonlinear incidence rates
state-dependent removal rate
Lyapunov functionals
global stability.
Article.18.pdf
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S. Wang, D. Zou, Global stability of in-host viral models with humoral immunity and intracellular delays, Appl. Math. Model., 36 (2012), 1313-1322
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H. Zhu, X. Zou, Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay, Discrete Contin. Dyn. Syst. Ser. B, 12 (2009), 511-524
]
Companion of Ostrowski-type inequality based on 5-step quadratic kernel and applications
Companion of Ostrowski-type inequality based on 5-step quadratic kernel and applications
en
en
The purpose of this paper is to establish an improved version of companion of Ostrowski's type integral
inequalities. The inequalities are obtained by using a newly developed special type of five steps quadratic
kernel. The introduction of this new Kernel gives some new error bounds for various quadrature rules.
Applications for composite quadrature rules and Cumulative Distributive Functions are considered.
537
552
Ather
Qayyum
Department of Fundamental and Applied Sciences
Universiti Teknologi PETRONAS
Malaysia
atherqayyum@gmail.com
Muhammad
Shoaib
Abu Dhabi Mens College
Higher Colleges of Technology
United Arab Emirates
safridi@gmail.com
Ibrahima
Faye
Department of Fundamental and Applied Sciences
Universiti Teknologi PETRONAS
Malaysia
ibrahima faye@petronas.com.my
Ostrowski inequality
numerical integration
composite quadrature rule
cumulative distributive function.
Article.19.pdf
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[1]
M. W. Alomari , A companion of Ostrowski's inequality with applications, Transylv. J. Math. Mech., 3 (2011), 9-14
##[2]
M. W. Alomari, A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications numerical integration , Kragujevac J. Math., 36 (2012), 77-82
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N. S. Barnett, S. S. Dragomir, I. Gomma, A companion for the Ostrowski and the generalized trapezoid inequalities, J. Math. Comput. Model., 50 (2009), 179-187
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A. Qayyum, I. Faye, M. Shoaib, M. A. Latif, A generalization of Ostrowski type inequality for mappings whose second derivatives belong to \(L_1(a; b)\) and applications, Inter. J. Pure Appl. Math., 98 (2015), 169-180
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A. Qayyum, S. Hussain, A new generalized Ostrowski Grüss type inequality and applications, Appl. Math. Lett., 25 (2012), 1875-1880
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A. Qayyum, M. Shoaib, I. Faye, Some new generalized results on Ostrowski type integral inequalities with application, J. Comput. Anal. Appl., 19 (2015), 693-712
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A. Qayyum, M. Shoaib, I. Faye, On new weighted Ostrowski type inequalities involving integral means over end intervals and application, Turkish J. Anal. Number Theory, 3 (2015), 61-67
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A. Qayyum, M. Shoaib, M. A. Latif , A generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications, Appl. Math. Sci., 8 (2014), 1889-1901
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A. Qayyum, M. Shoaib, A. E. Matouk, M. A. Latif, On new generalized Ostrowski type integral inequalities, Abstr. Appl. Anal., 2014 (2014), 1-8
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N. UJević, New bounds for the first inequality of Ostrowski-Grüss type and applications, Comput. Math. Appl., 46 (2003), 421-427
]
Analysis of a stochastic food chain model with finite delay
Analysis of a stochastic food chain model with finite delay
en
en
A stochastic three species predator-prey time-delay chain model is proposed and analyzed. Sufficient conditions
for persistence in time average and non-persistence are established. Numerical simulations are carried
out to support our results.
553
567
Jing
Fu
School of Mathematics
Changchun Normal University
P. R. China
Haihong
Li
Department of Basic Courses
Air Force Aviation University
P. R. China
Qixing
Han
School of Mathematics
Changchun Normal University
P. R. China
hanqixing123@163.com
Haixia
Li
School of Business
Northeast Normal University
P. R. China
Stochastic differential equation
persistent
non-persistent.
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]
Existence and uniqueness for solutions of parabolic quasi-variational inequalities with impulse control and nonlinear source terms
Existence and uniqueness for solutions of parabolic quasi-variational inequalities with impulse control and nonlinear source terms
en
en
In this paper, we present a new proof for the existence and uniqueness of solutions of parabolic quasivariational
inequalities with impulse control. We prove some properties of the presented algorithm (see [S.
Boulaaras, M. Haiour, Appl. Math. Comput., 217 (2011), 6443-6450], [S. Boulaaras, M. Haiour, Indaga.
Math., 24 (2013), 161-173]) using a semi-implicit scheme with respect to the t-variable combined with a
finite element spatial approximation.
568
583
Salah
Boulaaras
Department Of Mathematics, College Of Sciences and Arts
Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO)
Al-Qassim University
University of Oran 1
Kingdom Of Saudi Arabia
Algeria
saleh_boulaares@yahoo.fr
Parabolic quasi-variational inequality
finite elements
semi-implicit scheme
contraction
fixed point
impulse control problem.
Article.21.pdf
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]
Caristis fixed point theorem on \(C^*\)-algebra valued metric spaces
Caristis fixed point theorem on \(C^*\)-algebra valued metric spaces
en
en
We present the extension of Caristi's fixed point theorem for mappings defined on \(C^*\)-algebra valued metric
spaces. We prove the existence of fixed point using the concept of minimal element in \(C^*\)-algebra valued
metric space by introducing the notion of partial order on X.
584
588
Dur-e
Shehwar
Department of Mathematics
Capital University of Science and Technology
Pakistan
d.e.shehwar@jinnah.edu.pk
Samina
Batul
Department of Mathematics
Capital University of Science and Technology
Pakistan
samina.batul@jinnah.edu.pk
Tayyab
Kamran
Department of Mathematics
Quaid-i-Azam University
Pakistan
tayyabkamran@gmail.com
Adrian
Ghiura
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
adrianghiura25@gmail.com
Caristi's theorem
\(C^*\)-algebra
metric space.
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Z. Ma, L. Jiang, H. Sun, \(C^*\)-algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 1-11
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G. J. Murphy, \(C^*\)-Algebras and Operator Theory, Academic Press, Boston (1990)
]
The existence of solution for a stochastic fourth-order parabolic equation
The existence of solution for a stochastic fourth-order parabolic equation
en
en
The authors consider stochastic equations of the prototype
\[du + (
\gamma D^4u -
\gamma D^2f'(u) + D^2u - f'(u))dt - dw = 0;\]
where
\(\gamma>0\) is a constant and \(w\) is a \(Q\)-Wiener process in a probability space \((
\Omega;F; P)\). We establish the
global existence and uniqueness of the solution for this prototype in one dimension space. The random
attractor is also discussed.
589
602
Changchun
Liu
School of Mathematics
Jilin University
China
liucc@jlu.edu.cn
Jiaojiao
Wang
School of Mathematics
Jilin University
China
mathche@163.com
Random term
stochastic fourth-order equation
global existence.
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]
Existence and controllability of fractional stochastic neutral functional integro-differential systems with state-dependent delay in Fréchet spaces
Existence and controllability of fractional stochastic neutral functional integro-differential systems with state-dependent delay in Fréchet spaces
en
en
This paper investigates the existence and uniqueness of solutions of mild solutions for a fractional stochastic
neutral functional integro-differential equation with state-dependent delay in Fréchet spaces. The main
techniques rely on the fractional calculus, properties of characteristic solution operators and fixed point
theorems. Since we do not assume the characteristic solution operators are compact, our theorems guarantee
the effectiveness of controllability results in the infinite dimensional spaces.
603
616
Zuomao
Yan
Department of Mathematics
Hexi University
P. R. China
yanzuomao@163.com
Fangxia
Lu
Department of Mathematics
Hexi University
P. R. China
zhylfx@163.com
Fractional neutral stochastic integro-differential equations
fractional derivatives and integrals
state-dependent delay
solution operator
fixed point theorem.
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K. Balachandran, J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Anal., 72 (2010), 4587-4593
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Necessary optimality conditions for DC infinite programs with inequality constraints
Necessary optimality conditions for DC infinite programs with inequality constraints
en
en
In this paper, we first recall the regularity conditions introduced by Sun in [X. K. Sun, J. Math. Anal. Appl.,
414 (2014), 590-611]. Then, by using these regularity conditions, we obtain some necessary optimality
conditions for \(\varepsilon\)-optimal solution and exact optimal solution of a DC infinite programming problem with
inequality constraints. Moreover, we also apply the obtained results to conic programming problems.
617
626
Xiang-Kai
Sun
College of Mathematics and Statistics
College of Automation
Chongqing Technology and Business University
Chongqing University
China
China
sxkcqu@163.com
Xiao-Le
Guo
School of Economics
Southwest University of Political Science and Law
China
xlguocqu@163.com
Jing
Zeng
College of Mathematics and Statistics
Chongqing Technology and Business University
China
yiyuexue219@163.com
DC infinite programming
regularity conditions
optimality
conic programming.
Article.25.pdf
[
[1]
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N. Dinh, B. S. Mordukhovich, T. T. A. Nghia, Qualification and optimality conditions for DC programs with infinite constraints, Acta Math. Vietnam., 34 (2009), 125-155
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N. Dinh, B. Mordukhovich, T. T. A. Nghia, Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs, Math. Program, 123 (2010), 101-138
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##[8]
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##[19]
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##[20]
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]
Numerical solution of nth order fuzzy initial value problems by six stages
Numerical solution of nth order fuzzy initial value problems by six stages
en
en
The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs)
involving n-th order ordinary differential equations. The idea is based on the formulation of the six stages
Runge-Kutta method of order five (RKM56) from crisp environment to fuzzy environment followed by the
stability deffnitions and the convergence proof. It is shown that the n-th order FIVP can be solved by
RKM56 by transforming the original problem into a system of first-order FIVPs. The results indicate that
the method is very effective and simple to apply. An efficient procedure is proposed of RKM56 on the basis
of the principles and definitions of fuzzy sets theory and the capability of the method is illustrated by solving
second-order linear FIVP involving a circuit model problem.
627
640
A.
Jameel
School of Quantitative Sciences
Universiti Utara Malaysia (UUM)
Malaysia
kakarotte79@gmail.com
N. R.
Anakira
Department of Mathematics, Faculty of Science and Technology
Irbid National University
Jordan
alanaghreh_nedal@yahoo.com
A. K.
Alomari
Department of Mathematics, Faculty of Science
Yarmouk University
Jordan
abdomari2008@yahoo.com
I.
Hashim
School of Mathematical Sciences
Universiti Kebangsaan Malaysia
Malaysia
ishak_h@ukm.edu.my
M. A.
Shakhatreh
Department of Mathematics, Faculty of Science
Yarmouk University
Jordan
Mali@yu.edu.jo
Fuzzy numbers
fuzzy differential equations
circuit model problem
six stages Runge-Kutta method of order five.
Article.26.pdf
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]
A viscosity method for solving convex feasibility problems
A viscosity method for solving convex feasibility problems
en
en
In this paper, generalized equilibrium problems and strict pseudocontractions are investigated based on a
viscosity algorithm. Strong convergence theorems are established in the framework of real Hilbert spaces.
641
651
Yunpeng
Zhang
College of Electric Power
North China University of Water Resources and Electric Power
China
zhangypliyl@yeah.net
Yanling
Li
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power University
China
hsliyl@sina.com
Equilibrium problem
variational inequality
nonexpansive mapping
fixed point
viscosity algorithm.
Article.27.pdf
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[1]
B. A. Bin Dehaish, A. Latif, H. Bakodah, X. Qin , A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 1-14
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]
Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\)
Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\)
en
en
In this paper, we consider the following Schrödinger-Kirchhoff-type problem
\[
\begin{cases}
-(a+b\int_{R^N}|\nabla u|^2 dx)\Delta u+V(x)u=g(x,u) \,\,&\hbox{for} \,\,x\in R^N,\qquad (1.1)\\
u(x)\rightarrow 0 \,\,&\hbox{as} \,\,|x|\rightarrow\infty,
\end{cases}
\]
where constants \(a > 0; b \geq 0, N = 1; 2\) or \(3, V \in C(R^N;R), g \in C(R^N \times R;R)\). Under more relaxed
assumptions on \(g(x; u)\), by using some special techniques, a new existence result of infinitely many energy
solutions is obtained via Symmetric Mountain Pass Theorem.
652
660
Bitao
Cheng
School of Mathematics and Information Science
School of Mathematics and Statistics
Qujing Normal University
Central South University
P. R. China
P. R. China
chengbitao2006@126.com
Xianhua
Tang
School of Mathematics and Statistics
Central South University
P. R. China
tangxh@csu.edu.cn
Schrödinger-Kirchhoff type problem
critical point
symmetric Mountain Pass Theorem
variational methods.
Article.28.pdf
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L. Wang , On a quasilinear Schrödinger-Kirchhoff-type equations with radial potentials, Nonlinear Anal., 83 (2013), 58-68
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J. Wang, L. Tian, J. Xu, F. Zhang, Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth, J. Differential Equations, 253 (2012), 2314-2351
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X. Wu, Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(R^N\), Nonlinear Anal. RWA, 12 (2011), 1278-1287
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Y. Ye, C. Tang, Multiple solutions for Kirchhoff-type equations in \(R^N\), J. Math. Phys., 54 (2013), 1-16
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]
Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy
Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy
en
en
This paper is dedicated to provide explicit theta function representation of algebro-geometric solutions for
the generalized nonlinear Schrödinger hierarchy. Our main tools include zero-curvature equation to derive
the generalized nonlinear Schrödinger hierarchy, the hyper-elliptic curve with genus of N, the Abel-Jacobi
coordinates, the meromorphic function, the Baker-Akhiezer functions, and the Dubrovin-type equations for
auxiliary divisors. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions,
the meromorphic function, and the algebro-geometric solutions are obtained for the whole generalized
nonlinear Schrödinger hierarchy.
661
676
Qian
Li
Department of Mathematics
Shanghai University
China
Tiecheng
Xia
Department of Mathematics
Shanghai University
China
xiatc@shu.edu.cn
Chao
Yue
College of Information Engineering
Taishan Medical University
China
Algebro-geometric solutions
Abel-Jacobi coordinates
meromorphic function
Dubrovin-type equations
generalized nonlinear Schrödinger hierarchy.
Article.29.pdf
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Symmetric identities for degenerate generalized Bernoulli polynomials
Symmetric identities for degenerate generalized Bernoulli polynomials
en
en
In this paper, we give some interesting identities of symmetry for degenerate generalized Bernoulli polynomials attached to \(\chi\) which are derived from the properties of symmetry of certain p-adic invariant integrals
on \(\mathbb{Z}_p\).
677
683
Taekyun
Kim
Department of Mathematics, College of Science
Department of Mathematics
Tianjin Polytechnic University
Kwangwoon University
China
Republic of Korea
tkkim@kw.ac.kr
Dmitry V.
Dolgy
Institute of Natural Sciences
Far Eastern Federal University
Russaia
d_dol@mail.ru
Dae San
Kim
Department of Mathematics
Sogang University
Republic of Korea
dskim@sogang.ac.kr
Symmetry
identity
degenerate generalized Bernoulli polynomial.
Article.30.pdf
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]
Stability analysis of general viral infection models with humoral immunity
Stability analysis of general viral infection models with humoral immunity
en
en
We present two nonlinear viral infection models with humoral immune response and investigate their global
stability. The first model describes the interaction of the virus, uninfected cells, infected cells and B cells.
This model is an improvement of some existing models by incorporating more general nonlinear functions
for: (i) the intrinsic growth rate of uninfected cells; (ii) the incidence rate of infection; (iii) the removal rate of
infected cells; (iv) the production, death and neutralize rates of viruses; (v) the activation and removal rate
of B cells. In the second model, we introduce an additional population representing the latently infected
cells. The latent-to-active conversion rate is also given by a more general nonlinear function. For each
model, we derive two threshold parameters and establish a set of conditions on the general functions which
are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and
LaSalle's invariance principle, we prove the global asymptotic stability of all equilibria of the models.
684
704
A. M.
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
N. H.
AlShamrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
nalshmrane@kau.edu.sa
Viral infection
global stability
humoral immune response
Lyapunov function.
Article.31.pdf
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]
Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions
Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions
en
en
In this paper, we establish some new Hermite-Hadamard inequalities for s-convex functions via fractional
integrals. Some Hermite-Hadamard type inequalities for products of two convex and s-convex functions via
Riemann-Liouville integrals are also established.
705
716
Feixiang
Chen
Key Laboratory for Nonlinear Science and System Structure
Chongqing Three Georges University
P. R. China
cfx2002@126.com
Shanhe
Wu
Department of Mathematics and Computer Science
Longyan University
P. R. China
shanhewu@gmail.com
Hermite-Hadamard inequality
s-convex function
Riemann-Liouville fractional integrals
Article.32.pdf
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]