]>
2017
10
11
ISSN 2008-1898
547
Hybrid function projective synchronization in discrete dynamical networks via adaptive control
Hybrid function projective synchronization in discrete dynamical networks via adaptive control
en
en
In this paper, we study the hybrid function projective synchronization between coupled complex discrete networks with different dimensions.
The hybrid function projective synchronization is achieved by designing an adaptive control method. Based on the designed controller and the Lyapunov stability theory, we derive sufficient conditions to realize the hybrid function projective synchronization with different nodes. Moreover, with the adaptive update law, an adaptive control gains are obtained. Furthermore, we examine different cases of outer coupling matrix of node dynamics. Finally, we provide numerical examples to show the effectiveness of the proposed control scheme.
5593
5607
Ghada
Al-mahbashi
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
mahbashighada@yahoo.com
M. S. Md
Noorani
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.my
Sakhinah
Abu Bakar
School of mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
sakhinah@ukm.my
Hybrid function projective synchronization
delay coupling and non-delay coupling
discrete complex dynamical networks
adaptive control
Article.1.pdf
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[1]
G. Al-mahbashi, M. S. M. Noorani, S. A. Bakar, Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control, Nonlinear Dynam., 82 (2015), 1569-1579
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G. Al-mahbashi, M. S. M. Noorani, S. A. Bakar , Hybrid function projective synchronization of uncertain discrete complex dynamical networks, Int. J. Dynam. Control, 2016 (2016), 1-9
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]
Anti-synchronization of fractional-order chaotic complex systems with unknown parameters via adaptive control
Anti-synchronization of fractional-order chaotic complex systems with unknown parameters via adaptive control
en
en
This paper is concerned with adaptive control for anti-synchronization of a class of uncertain fractional-order chaotic complex systems described by a unified mathematical expression.
By utilizing the recently established result for the Caputo fractional derivative of a quadratic function
and employing the adaptive control technique, we design controllers and some fractional-order
parameter update laws
to anti-synchronize two fractional-order chaotic complex systems with unknown parameters.
The proposed method has generality, simplicity, and feasibility.
Moreover, anti-synchronization between uncertain fractional-order complex Lorenz system and fractional-order complex Lu system is implemented as an example to demonstrate the effectiveness and feasibility of the proposed scheme.
5608
5621
Cuimei
Jiang
School of Science
College of Mathematics and Systems Science
Qilu University of Technology
Shandong University of Science and Technology
P. R. China
P. R. China
jiangcuimei2004@163.com
Fangfang
Zhang
School of Electrical Engineering and Automation
Qilu University of Technology
P. R. China
zhff4u@163.com
Haiyong
Qin
School of Mathematics
Qilu Normal University
P. R. China
qhymath@163.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China
Linyi University
P. R. China
litongx2007@163.com
Adaptive control
anti-synchronization
fractional-order chaotic complex system
quadratic Lyapunov function
Article.2.pdf
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]
The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey
The stochastic interactions between predator and prey under Markovian switching: competitive interaction between multiple prey
en
en
In this paper, a class of
predator-prey model with prey competition is proposed, in which the interactions of predation between predator and prey are randomised and subsequently evaluated under Markovian switching. By constructing appropriate Lyapunov functions and applying various analytical methods, sufficient conditions for the existence of unique global positive solution, stochastic permanence and mean extinction are established. In the permanence case, we also estimate the superior and inferior limits of the sample path in a time-averaged Markov decision. We conclude that the interactions between predator and two prey, two competitive prey themselves and the dynamical properties of switching subsystems are not only dependent on subsystem coefficients but also on the transition probability of the Markov chain (switching from one state to another). Specific examples and numerical simulations are provided to demonstrate our theoretical results.
5622
5645
Yanqing
Li
College of Mathematics and System Sciences
Xinjiang University
P. R. China
1548510640@qq.com
Long
Zhang
College of Mathematics and System Sciences
Xinjiang University
P. R. China
Longzhang_xj@sohu.com
Random selection
competition between prey
Markovian switching
stochastic permanence
extinct in mean
Article.3.pdf
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]
Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance
Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance
en
en
This paper studies the robustness of global exponential stability of
neural networks evoked by deviating argument and stochastic
disturbance. Given the original neural network is globally
exponentially stable, we discuss the problem that the neural network
is still globally exponentially stable when the deviating argument
or both the deviating argument and stochastic disturbance is/are
generated. By virtue of solving the derived transcendental
equation(s), the upper bound(s) about the intensity of the deviating
argument or both of the deviating argument and stochastic
disturbance is/are received. The obtained theoretical results are
the supplements to the existing literatures on global exponential
stability of neural networks. Two numerical examples are offered to
demonstrate the effectiveness of theoretical results.
5646
5667
Liguang
Wan
College of Mechatronics and Control Engineering
Hubei Normal University
China
Ailong
Wu
College of Mathematics and Statistics
Hubei Normal University
China
hbnuwu@yeah.net
Jingru
Chen
Department of Personnel
Hubei Normal University
China
Global exponential stability
robustness
neural networks
deviating argument
stochastic disturbance
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H. Zhao, L. X. Li, H. P. Peng, J. Kurths, J. H. Xiao, Y. X. Yang , Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach, Eur. Phys. J. B, 88 (2015), 1-10
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]
Some fixed point theorems for \(\varphi\)-contractive mappings in fuzzy normed linear spaces
Some fixed point theorems for \(\varphi\)-contractive mappings in fuzzy normed linear spaces
en
en
In this paper a new concept of comparison function is introduced and discussed and some fixed point theorems are established for \(\varphi\)-contractive mappings in fuzzy normed linear spaces. In this way we obtain fuzzy versions of some classical fixed point theorems such as Nemytzki-Edelstein's theorem and Maia's theorem.
5668
5676
Sorin
Nădăban
Department of Mathematics and Computer Science
Aurel Vlaicu University of Arad
Romania
snadaban@gmail.com
Tudor
Bînzar
Department of Mathematics
Politehnica University of Timisoara
Romania
tudor.binzar@upt.ro
Flavius
Pater
Department of Mathematics
Politehnica University of Timisoara
Romania
flavius.pater@upt.ro
Fuzzy normed linear spaces
\(\varphi\)-contractive mappings
fixed point theorems
Article.5.pdf
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]
Study on differentiability problems of interval-valued functions
Study on differentiability problems of interval-valued functions
en
en
In this paper, we give the concepts of \(H\)-directional differentiability and \(D\)-directional differentiability of interval-valued functions. Then we discuss the properties of \(H\)-directional differentiable interval-valued functions and \(D\)-directional differentiable interval-valued functions. The necessary and sufficient conditions for the \(H\)-directional differentiability are given together with the sufficient conditions and the necessary and sufficient conditions for \(D\)-directional differentiability of interval-valued functions. Then we discuss the relationship between the two directional differentiability and prove these directional differentiability can be equivalent under a certain conditions.
5677
5689
Yu-E
Bao
College of Mathematics
Inner Mongolia University for Nationalities
P. R. China
byebed@163.com
Jin-Jun
Li
College of Mathematics
Inner Mongolia University for Nationalities
P. R. China
Eer-Dun
Bai
College of Computer Science and Technology
Inner Mongolia Universities
P. R. China
Hukuhara difference
Hausdorff distance
interval-valued function
\(H\)-directional differentiability
\(D\)-directional differentiability
Article.6.pdf
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[1]
Y. Chalco-Cano, H. Román-Flores, M. D. Jiménez-Gamero, Generalized derivative and \(\pi\)-derivative for set-valued functions, Inform. Sci., 181 (2011), 2177-2188
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Y. Chalco-Cano, A. Rufián-Lizan, H. Román-Flores, M. D. Jiménez-Gamero, Calculus for interval-valued functions using generalized Hukuhara derivative and applications, Fuzzy Sets and Systems, 219 (2013), 49-67
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V. Lupulescu , Fractional calculus for interval-valued functions, Fuzzy Sets and Systems, 265 (2015), 63-85
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R. Osuna-Gómez, Y. Chalco-Cano, B. Hernández-Jiménez, G. Ruiz-Garzón, Optimality conditions for generalized differentiable interval-valued functions, Inform. Sci., 321 (2015), 136-146
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L. Stefanini, B. Bede , Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal., 71 (2009), 1311-1328
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H.-C. Wu, The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective functions, European J. Oper. Res., 176 (2007), 46-59
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H.-C. Wu , The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions, European J. Oper. Res., 196 (2009), 49-60
]
Fixed points of weakly compatible mappings satisfying a generalized common limit range property
Fixed points of weakly compatible mappings satisfying a generalized common limit range property
en
en
In this paper, we produce new fixed point theorems for \(2n\) self-mappings \(\wp^a_1,\wp^a_2,\ldots,\wp^a_n\), \(\gamma^b_1,\gamma^b_2,\ldots,\gamma^b_n:\mathcal{X}\rightarrow\mathcal{X}\) on a metric space \((\mathcal{X},\rho )\), satisfying a generalized common limit range (CLR) property or CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\). Along with the newly introduced property CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\) for the \(2n\) self-mappings, we also assume that the pairs \((\wp^a_1,\gamma^b_1),(\wp^a_2,\gamma^b_2),\ldots,(\wp^a_n,\gamma^b_n)\) are weakly compatible. From the main result, we produce three more corollaries as its special cases. These results generalize the work of Sarwar et al. [M. Sarwar, M. Bahadur Zada, I. M. Erhan, Fixed Point Theory Appl., \({\bf 2015}\) (2015), 15 pages] and many others in the available literature. Two examples are also presented for the applications of our new FPTs.
5690
5700
Aziz
Khan
Department of Mathematics
University of Peshawar
Pakistan
azizkhan927@yahoo.com
Hasib
Khan
College of Engineering, Mechanics and Materials
Shaheed Benazir Bhutto University Sheringal
Hohai University
P. R. China
Pakistan
hasibkhan13@yahoo.com
Dumitru
Baleanu
Department of Mathematics
Institute of Space Sciences
Cankaya University
Turkey
Romania
dumitru@cankaya.edu.tr
Erdal
Karapinar
Department of Mathematics
Atilim University
Turkey
erdalkarapinar@yahoo.com
Tahir Saeed
Khan
Department of Mathematics
University of Peshawar
Pakistan
tsk7@uop.edu.pk
Weakly compatible mappings
common limit range property
fixed point theorems
Article.7.pdf
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[1]
R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
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M. U. Ali, T. Kamran, On (\(\alpha,\psi\))-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 (2013), 1-7
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M. U. Ali, T. Kamran, E. Karapınar, An approach to existence of fixed points of generalized contractive multivalued mappings of integral type via admissible mapping, Abstr. Appl. Anal., 2014 (2014), 1-7
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H. Aydi, E. Karapınar, I. Ş. Yüce, Quadruple fixed point theorems in partially ordered metric spaces depending on another function, ISRN Appl. Math., 2012 (2012), 1-16
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D. Baleanu, R. P. Agarwal, H. Khan, R. A. Khan, H. Jafari , On the existence of solution for fractional differential equations of order \(3 < \delta_1\leq 4\), Adv. Differ. Equ., 2015 (2015), 1-9
##[7]
D. Baleanu, H. Jafari, H. Khan, S. J. Johnston, Results for mild solution of fractional coupled hybrid boundary value problems, Open Math., 13 (2015), 601-608
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D. Baleanu, H. Khan, H. Jafari, R. A. Khan, M. Alipour, On existence results for solutions of a coupled systemof hybrid boundary value problems with hybrid conditions, Adv. Difference Equ., 2015 (2015), 1-14
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N. Hussain, H. Isik, M. Abbas, Common fixed point results of generalized almost rational contraction mappings with an application, J. Nonlinear Sci. Appl., 9 (2016), 2273-2288
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H. Jafari, D. Baleanu, H. Khan, R. A. Khan, A. Khan , Existence criterion for the solutions of fractional order p-Laplacian boundary value problems, Bound. Value Probl., 2015 (2015), 1-10
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F.-F. Jiang, J. Sun , On the existence of discontinuous periodic solutions for a class of Linard systems with impulses, Appl. Math. Comput., 291 (2016), 259-265
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M. Jleli, B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., 2015 (2015), 1-14
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H. Khan, H. Jafari, D. Baleanu, R. A. Khan, Aziz Khan, On iterative solutions and error estimations of a coupled system of fractional order differential-integral equations with initial and boundary conditions, Differ. Equ. Dyn. Syst., 2017 (2017), 1-13
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X.-L. Liu, Quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property, Fixed Point Theory Appl., 2013 (2013), 1-18
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Z. Mustafa, E. Karapınar, H. Aydi , A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
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S. B. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969), 475-478
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M. Sarwar, M. Bahadur Zada, I. M. Erhan, Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations, Fixed Point Theory Appl., 2015 (2015), 1-15
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W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling, 55 (2012), 680-687
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M. Stojaković, L. Gajić, T. Došenović, B. Carić, Fixed point of multivalued integral type of contraction mappings, Fixed Point Theory Appl., 2015 (2015), 1-10
]
Hyers-Ulam stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales
Hyers-Ulam stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales
en
en
This paper proves the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of nonlinear impulsive Volterra integro-delay dynamic system on time scales via a fixed point approach. The uniqueness and existence of the solution of nonlinear impulsive Volterra integro-delay dynamic system is proved with the help of Picard operator. The main tools for proving our results are abstract Gronwall lemma and Banach contraction principle. We also make some assumptions along with Lipschitz condition which make our results appropriate for the approach we are
using.
5701
5711
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
zadababo@yahoo.com;akbarzada@uop.edu.pk
Syed Omar
Shah
Department of Mathematics
University of Peshawar
Pakistan
omarshah89@yahoo.com;omarshahstd@uop.edu.pk
Yongjin
Li
Department of Mathematics
Sun Yat-sen University
P. R. China
stslyj@mail.sysu.edu.cn
Hyers-Ulam stability
Hyers-Ulam-Rassias stability
time scale
nonlinear Volterra integro-delay dynamic system
Article.8.pdf
[
[1]
R. P. Agarwal, A. S. Awan, D. O’Regan, A. Younus , Linear impulsive Volterra integro-dynamic system on time scales, Adv. Difference Equ., 2014 (2014), 1-17
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S. András, A. R. Mészáros, Ulam-Hyers stability of dynamic equations on time scales via Picard operators, Appl. Math. Comput., 209 (2013), 4853-4864
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J. J. Dacunha , Stability for time varying linear dynamic systems on time scales, J. Comput. Appl. Math., 176 (2005), 381-410
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A. E. Hamza, K. M. Oraby , Stability of abstract dynamic equations on time scales, Adv. Difference Equ., 2012 (2012), 1-15
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D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222-224
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S.-M. Jung, Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients, J. Math. Anal. Appl., 320 (2006), 549-561
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S.-M. Jung, J. Roh , The linear differential equations with complex constant coefficients and Schrödinger equations, Appl. Math. Lett., 66 (2017), 23-29
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Y.-J. Li, Y. Shen, Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett., 23 (2010), 306-309
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T.-X. Li, A. Zada , Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded linear operators over Banach spaces, Adv. Difference Equ., 2016 (2016), 1-8
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M. Obłoza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat., 13 (1993), 259-270
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I. A. Rus, Gronwall lemmas: ten open problems, Sci. Math. Jpn., 70 (2009), 221-228
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A. Zada, W. Ali, S. Farina, Hyers-Ulam stability of nonlinear differential equations with fractional integrable impulses, Math. Methods Appl. Sci., 40 (2017), 5502-5514
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A. Zada, S. Faisal, Y.-J. Li , On the Hyers-Ulam stability of first-order impulsive delay differential equations, J. Funct. Spaces, 2016 (2016), 1-6
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A. Zada, T.-X. Li, S. Ismail, O. Shah, Exponential dichotomy of linear autonomous systems over time scales, Diff. Equa. Appl., 8 (2016), 123-134
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A. Zada, S. O. Shah, S. Ismail, T.-X. Li, Hyers-Ulam stability in terms of dichotomy of first order linear dynamic systems , Punjab Univ. J. Math., 49 (2017), 37-47
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A. Zada, O. Shah, R. Shah , Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems, Appl. Math. Comput., 271 (2015), 512-518
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A. Zada, F. Ullah Khan, U. Riaz, T.-X. Li , Hyers-Ulam stability of linear summation equations, Punjab Univ. J. Math., 49 (2017), 19-24
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A. Zada, P. Wang, D. Lassoued, T.-X. Li, Connections between Hyers-Ulam stability and uniform exponential stability of 2-periodic linear nonautonomous systems , Adv. Difference Equ., 2017 (2017), 1-7
]
Viscosity regularization iterative methods and convergence analysis
Viscosity regularization iterative methods and convergence analysis
en
en
In this paper, a Moudafi's type viscosity regularization iterative method is introduced and investigated for an \(m\)-accretive mapping and a nonexpansive mapping. Strong convergence of the regularization iterative method is obtained in the framework of real uniformly smooth Banach spaces. Some subresults are also provided as applications of the main results.
5712
5722
Dongfeng
Li
School of Information Engineering
North China University of Water Resources and Electric Power
China
yslidf@yeah.net
Juan
Zhao
School of Mathematics and Statistics
North China University of Water Resources and Electric Power
China
zhaojuanyu@126.com
Accretive mapping
regularization iteration
uniform smoothness
operator equation
Article.9.pdf
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[1]
I. K. Argyros, S. George, S. M. Erappa, Expanding the applicability of the generalized Newton method for generalized equations, Commun. Optim. Theory, 2017 (2017), 1-12
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V. Barbu , Nonlinear semigroups and differential equations in Banach spaces, Translated from the Romanian, Editura Academiei Republicii Socialiste Romania, Bucharest; Noordhoff International Publishing, Leiden (1976)
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L.-C. Ceng, C.-F. Wen, Y.-H. Yao, Iteration approaches to hierarchical variational inequalities for infinite nonexpansive mappings and finding zero points of m-accretive operators, J. Nonlinear Var. Anal., 1 (2017), 213-235
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O. Chadli, A. Koukkous, A. Saidi , Existence of anti-periodic solutions for nonlinear implicit evolution equations with time dependent pseudomonotone operators, J. Nonlinear Var. Aanl., 1 (2017), 71-88
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S.-S. Chang, Some problems and results in the study of nonlinear analysis, Proceedings of the Second World Congress of Nonlinear Analysts, Part 7, Athens, (1996), Nonlinear Anal., 30 (1997), 4197-4208
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S.-S. Chang, H. W. J. Lee, C. K. Chan, Strong convergence theorems by viscosity approximation methods for accretive mappings and nonexpansive mappings, J. Appl. Math. Inform., 27 (2009), 59-68
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S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427-438
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S. Y. Cho, X.-L. Qin, L. Wang , Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
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Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions
Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions
en
en
In this paper, we introduce the notion of \(\theta\)-\(\phi\) \({C}\)-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.
5723
5733
Dingwei
Zheng
College of Mathematics and Information Science
Guangxi University
P. R. China
dwzheng@gxu.edu.cn
Xinhe
Liu
College of Mathematics and Information Science
Guangxi University
P. R. China
xhlwhl@gxu.edu.cn
Gengrong
Zhang
College of Mathematics and Computationl Science
Hunan First Normal University
P. R. China
2127542014qq.com
Fixed point
coupled fixed point
complete metric space
\(\theta\)-\(\phi\) \({C}\)-contraction
Article.10.pdf
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[1]
F. Bojor , Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901
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]
Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals
Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals
en
en
In this paper, we study second-order \(m\)-point
difference boundary value problems on infinite intervals
\[
\left\{\begin{array}{l}
\Delta^{2}x(k-1)+f(k,x(k),\Delta x(k-1))=0,~k\in N,\\
x(0)=\sum\limits_{i=1}^{m-2}\alpha_{i}x(\eta_{i}),~\lim\limits_{k
\rightarrow\infty }\Delta x(k)=0,
\end{array}
\right.
\]
where \(N=\{1,2,\cdots\},\ f:N\times R^{2}\rightarrow R\)
is continuous, \(\alpha_{i}\in
R,~\sum\limits_{i=1}^{m-2}\alpha_{i}\neq1,~\eta_{i}\in
N,~0<\eta_{1}<\eta_{2}<\cdots<\infty\) and
\[\Delta x(k)=x(k+1)-x(k),\]
the nonlinear term is dependent in a difference of lower order on
infinite intervals. By using Leray-Schauder continuation theorem,
the existence of solutions are investigated. Finally, we give one
example to demonstrate the use of the main result.
5734
5743
Changlong
Yu
College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China
changlongyu@126.com
Jufang
Wang
College of Sciences
Hebei University of Science and Technology
P. R. China
wangjufang1981@126.com
Yanping
Guo
College of Sciences
Hebei University of Science and Technology
P. R. China
guoyanping65@126.com
Surong
Miao
College of Sciences
Hebei University of Science and Technology
P. R. China
Difference equation
boundary value problem
Leray-Schauder continuation theorem
infinite interval
Article.11.pdf
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[1]
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]
Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions
Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions
en
en
The purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzel\`{a}-Ascoli theorem. Finally, we present several numerical examples to explicate
the main results.
5744
5752
Yunru
Bai
Institute of Computer Science, Faculty of Mathematics and Computer Science
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science
Jagiellonian University
Neijiang Normal University
Poland
China
yunrubai@163.com
Hua
Kong
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science
Neijiang Normal University
China
konghua2008@126.com
Caputo-Hadamard derivative
fractional differential equations
upper and lower solutions
monotone sequences
Arzela-Ascoli theorem
Article.12.pdf
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[1]
D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus, Models and numerical methods, Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2012)
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A. Fiscella, P. Pucci, p-fractional Kirchhoff equations involving critical nonlinearities, Nonlinear Anal. Real World Appl., 35 (2017), 350-378
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A. Kubica, P. Rybka, K. Ryszewska, Weak solutions of fractional differential equations in non cylindrical domains, Nonlinear Anal. Real World Appl., 36 (2017), 154-182
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N. Pan, B.-L. Zhang, J. Cao, Degenerate Kirchhoff-type diffusion problems involving the fractional p-Laplacian, Nonlinear Anal. Real World Appl., 37 (2017), 56-70
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H.-G. Sun, W. Chen, C.-P. Li, Y.-Q. Chen, Finite difference schemes for variable-order time fractional diffusion equation, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 22 (2012), 1-16
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S.-D. Zeng, D. Baleanu, Y.-R. Bai, G.-C. Wu , Fractional differential equations of Caputo-Katugampola type and numerical solutions, Appl. Math. Comput., 315 (2017), 549-554
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]
Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response
Dynamics of a diffusive viral model with Beddington-DeAngelis incidence rate and CTL immune response
en
en
In this paper, a four-dimensional system of viral model with cytotoxic lymphocyte (CTL) immune response is investigated. This model is a reaction-diffusion system with
Beddington-DeAngelis incidence rate and free diffusion in a bounded domain. With the help of comparison principle and Lyapunov function method, the well-posedness of solutions and sufficient conditions for global stability of nonnegative equilibria are established. It can be found that free diffusion has no influence on the global stability of the system with homogeneous Neumann boundary conditions.
5753
5762
Kejun
Zhuang
School of Statistics and Applied Mathematics
Anhui University of Finance and Economics
China
zhkj123@163.com
Viral model
global stability
Beddington-DeAngelis incidence rate
CTL immune response
Article.13.pdf
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[1]
N. C. Chí, E. ÁvilaVales, G. García Almeida , Analysis of a HBV model with diffusion and time delay, J. Appl. Math., 2012 (2012), 1-25
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K.-F. Wang, A.-J. Fan, A. Torres , Global properties of an improved hepatitis B virus model , Nonlinear Anal. Real World Appl., 11 (2010), 3131-3138
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X. Wang, Y.-D. Tao, X.-Y. Song, Global stability of a virus dynamics model with Beddington-DeAngelis incidence rate and CTL immune response, Nonlinear Dynam., 66 (2011), 825-830
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Y.-Y. Zhang, Z.-T. Xu , Dynamics of a diffusive HBV model with delayed Beddington-DeAngelis response, Nonlinear Anal. Real World Appl., 15 (2014), 118-139
]
Fixed point theorems in fuzzy cone metric spaces
Fixed point theorems in fuzzy cone metric spaces
en
en
In this paper we prove some fixed point theorems in fuzzy cone metric spaces under some fuzzy cone contractive type conditions. Our results generalize the ``fuzzy cone Banach contraction theorem'' given by [T. Oner, M. B. Kandemire, B. Tanay, J. Nonlinear Sci. Appl., \(\textbf{8}\) (2015), 610--616] recently.
5763
5769
Saif Ur
Rehman
Department of Mathematics
Sichuan University
P. R. China
saif.urrehman27@yahoo.com
Hong-Xu
Li
Department of Mathematics
Sichuan University
P. R. China
hoxuli@scu.edu.cn
Fixed point
fuzzy cone metric space
contraction condition
Article.14.pdf
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[1]
M. Abbas, M. Ali Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
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A. M. Ali, G. R. Kanna, Intuitionistic fuzzy cone metric spaces and fixed point theorems, Internat. J. Math. Appl., 5 (2017), 25-36
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F. Kiany, A. Amini-Haradi, Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-9
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A. Latif, N. Hussain, J. Ahmad, Coincidence points for hybrid contractions in cone metric spaces, J. Nonlinear Convex Anal., 17 (2016), 899-906
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Z.-L. Li, S.-J. Jiang, Quasi-contractions restricted with linear bounded mappings in cone metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-10
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Weighted Simpson type inequalities for \(h\)-convex functions
Weighted Simpson type inequalities for \(h\)-convex functions
en
en
In this paper we establish some weighted Simpson type inequalities
for functions whose derivatives in absolute value are \(h\)-convex.
5770
5780
Marian
Matłoka
Department of Applied Mathematics
Poznań University of Economics
Poland
marian.matloka@ue.poznan.pl
Simpson inequality
weighted inequalities
\(h\)-convex function
Article.15.pdf
[
[1]
M. Alomari, M. Darus, S. S. Dragomir, New inequalities of Simpson’s type for s-convex functions with applications, Res. Rep. Coll., 12 (2009), 1-18
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M. Alomari, S. Hussain, Two inequalities of Simpson type for quasi-convex functions and applications, Appl. Math. E-Notes, 11 (2011), 110-117
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E. Set, E. Özdemir, M. Z. Sarikaya, On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang J. Math., 42 (2012), 357-364
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K.-L. Tseng, G.-S. Yang, S. S. Dragomir , On weighted Simpson type inequalities and applications, J. Math. Inequal., 1 (2007), 13-22
##[13]
S. Varošanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311
]
The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation
The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation
en
en
The aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation \[\left\{\begin{array}{ll}
\frac{\partial u}{\partial t}- a^{2}\Delta u+b\cdot\nabla u+cu=0,~~~(x,t)\in\mathbb{R}^{n}\times(0,+\infty),\\
u(x,0)=\varphi(x),~~~x\in\mathbb{R}^{n}.\end{array}\right.\] We conclude that
(i) it is Hyers-Ulam stable on any finite interval;
(ii) if $c\neq0 $, it is Hyers-Ulam stable on the semi-infinite interval;
(iii) if $c=0$, it is not Hyers-Ulam stable on the semi-infinite interval by using Fourier transformation.
Furthermore, our results can be applied to the mean square Hyers-Ulam stability of parabolic equations driven by an \(n\)-dimensional Brownian motion.
5781
5788
Xiangkui
Zhao
School of Mathematics and Physics
University of Science and Technology Beijing
China
zhaoxiangkui@126.com
Xiaojun
Wu
School of Mathematics and Physics
University of Science and Technology Beijing
China
Zhihong
Zhao
School of Mathematics and Physics
University of Science and Technology Beijing
China
Hyers-Ulam stability
parabolic equation
stochastic differential equations
Article.16.pdf
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[1]
M. R. Abdollahpour, R. Aghayari, M. T. Rassias, Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions , J. Math. Anal. Appl., 437 (2016), 605-612
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]
Inequalities via generalized \(\log m\)-convex functions
Inequalities via generalized \(\log m\)-convex functions
en
en
The main objective of this paper is to introduce and investigate a new class of
convex functions, which is called as generalized \(\log\)
\(m\)-convex function. Some new Hermite-Hadamard type of integral inequalities
via generalized \(\log\) \(m\)-convex functions are obtained.
Several special cases are also discussed.
5789
5802
Muhammad Aslam
Noor
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
noormaslam@gmail.com
Khalida Inayat
Noor
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
khalidan@gmail.com
Farhat
Safdar
Department of Mathematics
COMSATS Institute of Information Technology
Pakistan
farhat 900@yahoo.com
Muhammad Uzair
Awan
Department of Mathematics
Government College University
Pakistan
awan.uzair@gmail.com
Saleem
Ullah
Department of Mathematics
University of Islamabad
Pakistan
saleemullah314@hotmail.com
Generalized convex functions
generalized \(\log\) \(m\)-convex functions
Hermite-Hadamard type inequalities
Article.17.pdf
[
[1]
M. Alomari, M. Darus, S. S. Dragomir , New inequalities of Simpson’s type for s-convex functions with applications, Res. Rep. Coll., 12 (2009), 1-18
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M. R. Delavar, F. Sajadian, Hermite-Hadamard type integral inequalities for log-\(\eta\)-convex function , Math. Comput. Sci., 1 (2016), 86-92
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]
Approximation with modified Phillips operators
Approximation with modified Phillips operators
en
en
In the present paper, we study modified Phillips operators in simultaneous approximation. The operators discussed here are important as they have link with the well-known Szász operators. We estimate some direct results for the operators.
5803
5812
Danyal
Soybaş
Department of Mathematics Education, Faculty of Education
Erciyes University
Turkey
danyal@erciyes.edu.tr
Szász operators
Phillips operators
simultaneous approximation
modulus of continuity
moment generating function
asymptotic formula
error estimation
Article.18.pdf
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[1]
Z. Finta, V. Gupta, Direct and inverse estimates for Phillips type operators, J. Math. Anal. Appl., 303 (2005), 627-642
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S. G. Gal, V. Gupta, Complex form of a link operator between the Phillips and the Szász-Mirakjan operators, Results Math., 67 (2015), 381-393
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]
Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms
Asymptotic behavior of solutions to a class of coupled semilinear parabolic systems with gradient terms
en
en
This paper concerns the asymptotic behavior of solutions
to the Cauchy problem of a class of coupled semilinear parabolic systems with gradient terms.
Using the energy comparison method and comparison principle,
the blow-up theorem of Fujita type is established
and the critical Fujita curve is formulated by spacial dimension,
the behavior of the coefficient of the gradient term at infinity.
5813
5824
Yang
Na
School of Mathematics
Jilin University
P. R. China
Yuanyuan
Nie
School of Mathematics
Jilin University
P. R. China
Xu
Zhou
College of Computer Science and Technology
Jilin University
P. R. China
zhouxu0001@163.com
Asymptotic behavior
critical Fujita curve
gradient term
Article.19.pdf
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[1]
K. Deng, H. A. Levine, The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl., 243 (2000), 85-126
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W. Guo, M. Lei, Critical Fujita curves for a coupled reaction-convection-diffusion system with singular coefficients, J. Jilin Univ. Sci., 54 (2016), 183-188
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W. Guo, X. Wang, M. Zhou, Asymptotic behavior of solutions to a class of semilinear parabolic equations, Bound. Value Probl., 2016 (2016), 1-9
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M.-J. Zhou, H.-L. Li, W. Guo, X. Zhou , Critical Fujita exponents to a class of non-Newtonian filtration equations with fast diffusion, Bound. Value Probl., 2016 (2016), 1-16
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Q. Zhou, Y.-Y. Nie, X.-Y. Han, Large time behavior of solutions to semilinear parabolic equations with gradient , J. Dyn. Control Syst., 22 (2016), 191-205
]
Robust weighted expected residual minimization formulation for stochastic vector variational inequalities
Robust weighted expected residual minimization formulation for stochastic vector variational inequalities
en
en
In order to deal with (stochastic) multi-objective optimization problems, a robust Pareto optimal solution by minimizing the worst case weighted sum of
objectives on a given weight set is considered [J. Hu, S. Mehrotra, Oper. Res., \(\textbf{60}\) (2011), 936--953], [J. Hu, T. Homem-de-Mello, S. Mehrotra, Manuscript, (2010)]. Based on this idea, we introduce a new class of deterministic model for stochastic vector variational inequalities, called robust weighted expected residual minimization model. Then we propose sample average approximation (SAA) approach to solve robust weighted expected residual minimization problems. Some convergence results are established for the approximation
problem in terms of the optimal value and the set of optimal solutions.
5825
5833
Yong
Zhao
College of Mathematics and Statistics
Chongqing JiaoTong University
China
zhaoyongty@126.com
Zai Yun
Peng
College of Mathematics and Statistics
Chongqing JiaoTong University
China
pengzaiyun@126.com
Yun Bin
Zhao
School of Mathematics
University of Birmingham
UK
y.zhao.2@bham.ac.uk
Robust weighted expected residual minimization
stochastic vector variational inequalities
convergence
Article.20.pdf
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[1]
C. Charitha, J. Dutta, Regularized gap functions and error bounds for vector variational inequalities , Pac. J. Optim., 6 (2010), 497-510
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C. Charitha, J. Dutta, C. S. Lalitha , Gap functions for vector variational inequalities, Optimization, 64 (2015), 1499-1520
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X.-J. Chen, M. Fukushima , Expected residual minimization method for stochastic linear complementarity problems, Math. Oper. Res., 30 (2005), 1022-1038
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G.-Y. Chen, X.-X. Huang, X.-Q. Yang , Vector optimization, Set-valued and variational analysis, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin (2005)
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J. Hu, T. Homem-de-Mello, S. Mehrotra, Multi-criterion robust and stochastic dominance-constrained models with application to budget allocation in homeland security, Manuscript, (2010)
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J. Hu, S. Mehrotra, Robust and stochastically weighted multiobjective optimization models and reformulations, Oper. Res., 60 (2011), 936-953
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N. J. Huang, J. Li, X. Q. Yang, Weak sharpness for gap functions in vector variational inequalities, J. Math. Anal. Appl., 394 (2012), 449-457
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G.-H. Lin, M. Fukushima , Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: a survey, Pac. J. Optim., 6 (2010), 455-482
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Y.-C. Liu, H.-F. Xu, Stability analysis of stochastic programs with second order dominance constraints, Math. Program., 142 (2013), 435-460
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M.-J. Luo, G.-H. Lin , Convergence results of the ERM method for nonlinear stochastic variational inequality problems, J. Optim. Theory Appl., 142 (2009), 569-581
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M.-J. Luo, G.-H. Lin , Expected residual minimization method for stochastic variational inequality problems, J. Optim. Theory Appl., 140 (2009), 103-116
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M.-J. Luo, G.-H. Lin, Stochastic variational inequality problems with additional constraints and their applications in supply chain network equilibria, Pac. J. Optim., 7 (2011), 263-279
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R. T. Rockafellar, R.J.-B.Wets, Stochastic variational inequalities: single-stage to multistage, Math. Program., 165 (2017), 331-360
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M. Sofonea, Y.-B. Xiao, Fully history-dependent quasivariational inequalities in contact mechanics, Appl. Anal., 95 (2016), 2464-2484
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Y. Zhao, J. Zhang, X.-M. Yang, G.-H. Lin , Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities, J. Optim. Theory Appl., 175 (2017), 545-566
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Stability analysis for a delayed SIR model with a nonlinear incidence rate
Stability analysis for a delayed SIR model with a nonlinear incidence rate
en
en
We develop an SIR vector-bone epidemic model incorporating
incubation time delay and the nonlinear incidence rate, where the
growth of susceptibles is governed by the logistic equation. The
threshold parameter \(R_0\) is used to determine whether the disease
persists in the population. The model always has the trivial
equilibrium and the disease-free equilibrium whereas admits the
endemic equilibrium if \(R_0\) exceeds one. The disease-free
equilibrium is globally asymptotically stable if \(R_0\) is less than
one, while the system is persistent if \(R_0\) is greater than one.
Furthermore, by applying the time delay as a bifurcation parameter,
the local stability of the endemic equilibrium is discussed and it
loses stability and Hopf bifurcation occurs as the length of the
time delay increases past \(\tau_0\) under certain conditions. An
example is carried out to illustrate the main results.
5834
5845
Luju
Liu
School of Mathematics and Statistics
Henan University of Science and Technology
China
lujuliu@126.com
Yan
Wang
College of Science
China University of Petroleum
China
wangyan@upc.edu.cn
Stability analysis
delayed SIR model
nonlinear incidence rate
Lyapunov function
Hopf bifurcation
Article.21.pdf
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]
Split equality problem for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping in Hilbert space
Split equality problem for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping in Hilbert space
en
en
In this paper, we consider the split equality problem (SEP) in Hilbert space. We propose and investigate a new iterative
algorithm for solving split equality problem for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping. Finally, a numerical example is given to illustrate the feasibility of the proposed algorithm.
5846
5852
Ying
Chen
Statistical Research Institute
Tianjin University of Technology and education
Naikai University
China
China
18630852201@163.com
Haili
Guo
Department of Mathematics
Tianjin Polytechnic University
China
1101570027@qq.com
Luoyi
Shi
Department of Mathematics
Tianjin Polytechnic University
China
shiluoyi@tjpu.edu.cn
Zhaojun
Wang
Statistical Research Institute
Naikai University
China
zjwang@nankai.edu.cn
General split equality problem
\(\kappa\)-asymptotically strictly pseudo-nonspreading mapping
Hilbert space
Article.22.pdf
[
[1]
V. Berinde , Iterative Approximation of Fixed Points , Editura Efemeride, Baia Mare (2002)
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F. E. Browder, W. V. Petryshyn , Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20 (1967), 197-228
##[3]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[4]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov , A unified approach for inversion problems in intensity-modulated therapy, Phys. Medicine Biol., 51 (2006), 2353-2365
##[5]
S.-S. Chang, Y. J. Cho, J. K. Kim, W. B. Zhang, L. Yang, Multiple-set split feasibilty problems for asymptotically strict pseudocontractions, Abstr. Appl. Anal., 2012 (2012), 1-12
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R. D. Chen, J. Wang, H. Zhang, General split equality problems in Hilbert space, Fixed Point Theory Appl., 2014 (2014), 1-8
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A. Moudafi, A relaxed alternating CQ-algorithm for convex feasibility problems, Nonlinear Anal. Theory Meth. Appl., 79 (2013), 117-121
##[8]
A. Moudafi, Alternating CQ-algorithm for convex feasibility and split fixed point problems, J. Nonlinear Convex Anal., 15 (2014), 809-818
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J. Quan, S.-S. Chang, Multiple-set split feasibility problems for \(\kappa\)-asymptotically strictly pseudo-nonspreading mapping in Hilbert space, J. Inequal. Appl., 2014 (2014), 1-14
##[10]
L. Shi, R. D. Chen, Y. J. Wu, An iterative algorithm for the split equality and multiple-sets split equality problem, Abstr. Appl. Anal., (2014)
]
Fixed point theorems for \(C\)-class functions in \(b\)-metric spaces and applications
Fixed point theorems for \(C\)-class functions in \(b\)-metric spaces and applications
en
en
The aim of this paper is to present some fixed point results for \(C\)-class functions in the setting of \(b\)-metric spaces. Moreover, some examples are given to support the main results. In addition, by using our results, we obtain the existence and uniqueness of solution to differential or integral equation. Furthermore, for the differential equation, we provide the precise mathematical expression of solution.
5853
5868
Huaping
Huang
School of Mathematical Sciences
Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education
China
mathhhp@163.com
Guantie
Deng
School of Mathematical Sciences
Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education
China
denggt@mail.bnu.edu.cn
Stojan
Radenović
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.net
\(C\)-class function
\(b\)-metric space
fixed point
altering distance function
integral equation
Article.23.pdf
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J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei,W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)- contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-23
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W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b-metric spaces , J. Math. Anal., 7 (2016), 1-12
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W. Shatanawi, M. Postolache, A. H. Ansari, W. Kassab , Common fixed points of dominating and weak annihilators in ordered metric spaces via C-class functions, J. Math. Anal., 8 (2017), 54-68
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S. L. Singh, S. Czerwik, K. Król, A. Singh, Coincidences and fixed points of hybrid contractions, Stability of functional equations and applications, Tamsui Oxf. J. Math. Sci., 24 (2008), 401-416
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W. Sintunavarat, Fixed point results in b-metric spaces approach to the existence of a solution for nonlinear integral equations, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 110 (2016), 585-600
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W. Sintunavarat , Nonlinear integral equations with new admissibility types in b-metric spaces, J. Fixed Point Theory Appl., 18 (2016), 397-416
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O. Yamaod, W. Sintunavarat, Y. J. Cho , Common fixed point theorems for generalized cyclic contraction pairs in b-metric spaces with applications , Fixed Point Theory Appl., 2015 (2015), 1-18
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O. Yamaod, W. Sintunavarat, Y. J. Cho, Existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric spaces, Open Math., 14 (2016), 128-145
]
Generalized harmonically convex functions on fractal sets and related Hermite-Hadamard type inequalities
Generalized harmonically convex functions on fractal sets and related Hermite-Hadamard type inequalities
en
en
In this paper, the author introduced the concept of generalized harmonically convex function on fractal sets \(\mathbb{R}^{\alpha}(0<\alpha\leq1)\) of real line numbers and established generalized Hermite-Hadamard's inequalities for generalized harmonically convex function. Then, by creating a local fractional integral identity, obtained some Hermite-Hadamard type inequalities of these classes of functions.
5869
5880
Wenbing
Sun
School of Science
Shaoyang University
P. R. China
swb0520@163.com
Generalized harmonically convex function
Hermite-Hadamard type inequality
fractal space
local fractional integral
Article.24.pdf
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[1]
A. Akkurt, M. Z. Sarikaya, H. Budak, H. Yildirim, Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 111 (2017), 797-807
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M. W. Alomari, M. Darus, U. S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 1643-1652
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M. K. Bakula, M. E. Özdemir, J. Pečarić , Hadamard-type inequalities for m-convex and (\(\alpha,m\))-convex functions, J. Inequal. Pure Appl. Math., 2008 (2008), 1-12
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G. Chen, H. M. Srivastava, P. Wang, W. Wei, Some further generalizations of Hölder’s inequality and related results on fractal space, Abstr. Appl. Anal., 2014 (2014), 1-7
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L. Chun, F. Qi , Inequalities of Simpson type for functions whose third derivatives are extended s-convex functions and applications to means, J. Comput. Anal. Appl., 19 (2015), 555-569
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S. Erden, M. Z. Sarikaya, Generalized Pompeiu type inequalities for local fractional integrals and its applications, Appl. Math. Comput., 274 (2016), 282-291
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İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacet. J. Math. Stat., 43 (2014), 935-942
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M. A. Latif, M. Shoaib , Hermite-Hadamard type integral inequalities for differentiable m-preinvex and (\(\alpha,m\))-preinvex functions, J. Egyptian Math. Soc., 23 (2015), 236-241
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H. Mo, X. Sui, Hermite-Hadamard-type inequalities for generalized s-convex functions on real linear fractal set \(\mathbb{R}^\alpha (0 < \alpha < 1)\), Math. Sci., 11 (2017), 241-246
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H.-X. Mo, X. Sui, D.-G. Yu, Generalized convex functions on fractal sets and two related inequalities, Abstr. Appl. Anal., 2014 (2014), 1-7
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M. E. Özdemir, M. Avci, H. Kavurmaci , Hermite-Hadamard type inequalities via (\(\alpha,m\))-convexity , Comput. Math. Appl., 61 (2011), 2614-2620
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M. E. Özdemir, Ç. Yıldız, A. O. Akdemir, E. Set, On some inequalities for s-convex functions and applications, J. Inequal. Appl., 2013 (2013), 1-11
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S. Qaisar, C.-J. He, S. Hussain, A generalizations of Simpsons type inequality for differentiable functions using (\(\alpha,m\))- convex functions and applications, J. Inequal. Appl., 2013 (2013), 1-13
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M. Z. Sarikaya, H. Budak , Generalized Ostrowski type inequalities for local fractional integrals, Proc. Amer. Math. Soc., 145 (2017), 1527-1538
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W.-B. Sun, Q. Liu, New Hermite-Hadamard type inequalities for (\(\alpha,m\))-convex functions and applications to special means, J. Math. Inequal., 11 (2017), 383-397
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W. Sun, Q. Liu, New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications, J. Zhejiang Univ. Sci. A, 44 (2017), 47-52
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X.-J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong (2011)
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X.-J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York (2012)
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Y.-J. Yang, D. Baleanu, X.-J. Yang , Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys., 2013 (2013), 1-6
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X.-J. Yang, F. Gao, H. M. Srivastava , A new computational approach for solving nonlinear local fractional PDEs, J. Comput. Appl. Math., 339 (2018), 285-296
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X.-J. Yang, F. Gao, H. M. Srivastava, New rheological models within local fractional derivative, Rom. Rep. Phys., 2017 (2017), 1-12
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X.-J. Yang, F. Gao, H. M. Srivastava , Non-differentiable exact solutions for the nonlinear odes defined on fractal sets, Fractals, 2017 (2017), 1-9
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X.-J. Yang, J. T. Machado, C. Cattani, F. Gao, On a fractal LC-electric circuit modeled by local fractional calculus, Comm. Nonlinear Sci. Numer. Simulat., 47 (2017), 200-206
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X.-J. Yang, J. A. Tenreiro, D. Baleanu, Exact traveling-wave solution for local fractional Boussinesq equation in fractal domain, Fractals, 2017 (2017), 1-7
]
On the characterization of the solution set for vector equilibrium problem
On the characterization of the solution set for vector equilibrium problem
en
en
In this article, we investigate the nonemptiness and compactness
of the solution set for vector equilibrium problem defined in finite-dimensional spaces. We show that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set provided that \(R_1=\{0\}\) holds. Furthermore, we obtain that vector equilibrium problem has nonempty and compact solution set if and only if linearly scalarized equilibrium problem has nonempty and compact solution set when coercivity condition holds. As applications, we employ the obtained results to derive Levitin-Polyak well-posedness, stability analysis and connectedness of the solution set of the vector equilibrium problem.
5881
5895
Gang
Wang
School of Management Science
Qufu Normal University
China
wgglj1977@163.com
Lijun
Gao
School of Engineering
Qufu Normal University
China
gljwg1977@163.com
Vector equilibrium problem
nonemptiness and compactness
asymptotic cone
coercivity condition
Article.25.pdf
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Y. Han, N.-J. Huang , The connectedness of the solutions set for generalized vector equilibrium problems, Optimization, 65 (2016), 357-367
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Q.-Y. Liu, X.-J. Long, N.-J. Huang, Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems, Math. Slovaca, 62 (2012), 123-136
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I. Sadeqi, C. G. Alizadeh., Existence of solutions of generalized vector equilibrium problems in reflexive Banach spaces, Nonlinear Anal., 74 (2011), 2226-2234
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M. Sofonea, Y.-B. Xiao, Fully history-dependent quasivariational inequalities in contact mechanics, Appl. Anal., 95 (2016), 2464-2484
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G. Wang, Existence-stability theorems for strong vector set-valued equilibrium problems in reflexive Banach spaces, J. Inequal. Appl., 2015 (2015), 1-14
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G. Wang, X. X. Huang, Levitin-Polyak well-posedness for optimization problems with generalized equilibrium constraints, J. Optim. Theory Appl., 153 (2012), 27-41
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G. Wang, X. X. Huang, J. Zhang, Levitin-Polyak well-posedness in generalized equilibrium problems with functional constraints, Pac. J. Optimi., 6 (2010), 441-453
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Y.-M. Wang, Y.-B. Xiao, X. Wang, Y. J. Cho, Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems, J. Nonlinear. Sci. Appl., 9 (2016), 1178-1192
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Y.-B. Xiao, N.-J. Huang, Y. J. Cho, A class of generalized evolution variational inequalities in Banach space, Appl. Math. Lett., 25 (2012), 914-920
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]
Infinitely many periodic solutions for second-order discrete Hamiltonian systems
Infinitely many periodic solutions for second-order discrete Hamiltonian systems
en
en
Infinitely many periodic solutions are obtained for a second-order discrete Hamiltonian systems by using the minimax methods in critical point theory. Our results extend and improve previously known results.
5896
5903
Da-Bin
Wang
Department of Applied Mathematics
Lanzhou University of Technology
People's Republic of China
wangdb96@163.com
Qin
Xiao
Department of Applied Mathematics
Lanzhou University of Technology
People's Republic of China
1063838122@qq.com
Wen
Guan
Department of Applied Mathematics
Lanzhou University of Technology
People's Republic of China
mathguanw@163.com
Minimax methods
periodic solutions
sublinear
discrete Hamiltonian systems
critical point
Article.26.pdf
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[1]
C.-F. Che, X.-P. Xue, Infinitely many periodic solutions for discrete second-order Hamiltonian systems with oscillating potential, Adv. Difference Equ., 2012 (2012), 1-9
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Y.-F. Xue, C.-L. Tang, Existence and multiplicity of periodic solution for second-order discrete Hamiltonian systems, J. Southwest China Normal Uni., 31 (2006), 7-12
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Y.-F. Xue, C.-L. Tang, Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system, Nonlinear Anal., 67 (2007), 2072-2080
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]
A modified infeasible homotopy algorithm for computing fixed point in general non-convex set
A modified infeasible homotopy algorithm for computing fixed point in general non-convex set
en
en
In this paper, to find a fixed point of self-mapping in the general
non-convex set with both equality constraints and inequality
constraints, a modified infeasible homotopy for perturbing only
inequality constraints is constructed and the global convergence of
the smooth homotopy pathways is proved under some much weaker
conditions. The advantage of the modified homotopy is that the
initial point needs to be only in the shifted set with only
inequality constraints, not necessarily, a feasible point in the
original set, and hence it is more convenient to be implemented than
the existing methods. The feasibility and effectiveness of the
modified homotopy method is shown by some numerical tests.
5904
5913
Zhichuan
Zhu
School of Statistics
Jilin University of Finance and Economics
China
zhuzcnh@126.com
Ruifeng
Wu
School of Applied Mathematics
Jilin University of Finance and Economics
China
wuruifeng@jlufe.edu.cn
Yanchun
Xing
School of Statistics
Jilin University of Finance and Economics
China
xingyanchun778@163.com
Infeasible homotopy
fixed point
self-mapping
non-convex set
Article.27.pdf
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Y.-H. Yao, Y.-C. Liou, J.-C. Yao , Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction , Fixed Point Theory Appl., 2015 (2015), 1-19
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Z.-C. Zhu, B. Yu, Globally convergent homotopy algorithm for solving the KKT systems to the principal-agent bilevel programming, Optim. Methods Softw., 32 (2017), 69-85
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]
On a functional equation connected with bi-linear mappings and its Hyers-Ulam stability
On a functional equation connected with bi-linear mappings and its Hyers-Ulam stability
en
en
We introduce the notion of a bi-linear mapping which generalizes some known ones, and note that bi-linear mappings satisfy a functional equation. The Hyers-Ulam stability of this equation is studied in Banach, \(2\)-Banach and complete non-Archimedean normed spaces.
5914
5921
Krzysztof
Ciepliński
Faculty of Applied Mathematics
AGH University of Science and Technology
Poland
cieplin@agh.edu.pl
Hyers-Ulam stability
functional equation
system of functional equations
Article.28.pdf
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J.-H. Bae, W.-G. Park, On the solution of a bi-Jensen functional equation and its stability, Bull. Korean Math. Soc., 43 (2006), 499-507
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N. Brillouët-Belluot, J. Brzdęk, K. Ciepliński , On some recent developments in Ulam’s type stability, Abstr. Appl. Anal., 2012 (2012), 1-41
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M. S. Moslehian, T. M. Rassias , Stability of functional equations in non-Archimedean spaces , Appl. Anal. Discrete Math., 1 (2007), 325-334
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]
The split feasibility problems in an infinite dimensional space
The split feasibility problems in an infinite dimensional space
en
en
The purpose of this article is to investigate the approximation of common solutions of fixed point and split feasibility problems. A viscosity iterative algorithm is introduced and studied for this approximation problem. Strong convergence theorems are established in an infinite dimensional real Hilbert space.
5922
5931
Mingliang
Zhang
School of Mathematics and Statistics
Henan University
China
hdzhangml@yeah.net
Image reconstruction
approximation solution
viscosity method
split feasibility problem
Article.29.pdf
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H.-Y. Zhou, P.-Y. Wang, Adaptively relaxed algorithms for solving the split feasibility problem with a new step size, J. Inequal. Appl., 2014 (2014), 1-22
]
Strong convergence of Halpern method for firmly type nonexpansive mappings
Strong convergence of Halpern method for firmly type nonexpansive mappings
en
en
In this paper, Halpern method is applied to find fixed points of a
class of firmly type nonexpansive mappings. A strong convergence
result is obtained under the control conditions (C1) and (C2).
Our conclusion obtained in this paper gives the affirmative answer
of the Halpern open problem for this class of mapping.
5932
5938
Yonghong
Yao
Institute of Fundamental and Frontier Sciences
University of Electronic Science and Technology of China
China
yaoyonghong@aliyun.com
Mihai
Postolache
China Medical University
University Politehnica of Bucharest
Taiwan
Romania
emscolar@yahoo.com
Naseer
Shahzad
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nshahzad@kau.edu.sa
Fixed point
Halpern method
firmly type nonexpansive mappings
strong convergence
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Y.-L. Cui, X. Liu , Notes on Browder’s and Halpern’s methods for nonexpansive maps, Fixed Point Theory, 10 (2009), 89-98
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Y.-H. Yao, R.-D. Chen, J.-C. Yao, Strong convergence and certain control conditions for modified Mann iteration, Nonlinear Anal., 68 (2008), 1687-1693
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Y.-H. Yao, Y.-C. Liou, T.-L. Lee, N.-C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal., 17 (2016), 655-668
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Y.-H. Yao, M. Postolache, S. M. Kang , Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory Appl., 2014 (2014), 1-13
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Y.-H. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings , Fixed Point Theory Appl., 2015 (2015), 1-15
]
A fixed point theorem for systems of operator equations and its application
A fixed point theorem for systems of operator equations and its application
en
en
A new fixed point theorem in product cones is established for systems of
operator equations, where the components are expressed by partial ordering. In applications, this allows the nonlinear term
of a differential system to have different behaviors in components.
5939
5946
Yujun
Cui
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology
Shandong University of Science and Technology
P. R. China
cyj720201@163.com
Fixed point theorem
differential system
partial order
Article.31.pdf
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R. P. Agarwal, N. Hussain, M.-A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations , Abstr. Appl. Anal., 2012 (2012), 1-15
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X. Cheng, Existence of positive solutions for a class of second-order ordinary differential systems, Nonlinear Anal., 69 (2008), 3042-3049
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]
Certain Ostrowski type inequalities for generalized \(s\)-convex functions
Certain Ostrowski type inequalities for generalized \(s\)-convex functions
en
en
In this paper, we first obtain a generalized integral identity for twice local
differentiable functions. Then, using functions whose second derivatives in absolute value
at certain powers are generalized \(s\)-convex in the second sense, we obtain some new Ostrowski type inequalities.
5947
5957
Muharrem
Tomar
Department of Mathematics, Faculty of Arts and Sciences
Ordu University
Turkey
muharremtomar@gmail.com
Praveen
Agarwal
Department of Mathematics
Department of Mathematics
Anand International College of Engineering
Ahi Evran University
India
Turkey
goyal.praveen2011@gmail.com
Mohamed
Jleli
Department of Mathematics
King Saud University
Saudi Arabia
jleli@ksu.edu.sa
Bessem
Samet
Department of Mathematics
King Saud University
Saudi Arabia
bsamet@ksu.edu.sa
Generalized \(s\)-convex functions
generalized Hermite-Hadamard inequality
generalized Hölder inequality
Article.32.pdf
[
[1]
P. Agarwal , Some inequalities involving Hadamard-type k-fractional integral operators, Math. Methods Appl. Sci., 40 (2017), 3882-3891
##[2]
P. Agarwal, M. Jleli, M. Tomar, Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals, J. Inequal. Appl., 2017 (2017), 1-10
##[3]
H. Budak, M. Z. Sarikaya, H. Yildirim, New inequalities for local fractional integrals, RGMIA Research Report Collection, 18 (2015), 1-13
##[4]
J.-S. Choi, E. Set, M. Tomar , Certain generalized Ostrowski type inequalities for local fractional integrals, Commun. Korean Math. Soc., 32 (2017), 601-617
##[5]
S. Erden, M. Z. Sarikaya, Generalized Pompeiu type inequalities for local fractional integrals and its applications, Appl. Math. Comput., 247 (2016), 282-291
##[6]
M. A. Latif, Inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are convex with applications, Arab J. Math. Sci., 21 (2015), 84-97
##[7]
H.-X. Mo , Generalized Hermite-Hadamard inequalities involving local fractional integral, ArXiv, 2014 (2014), 1-8
##[8]
H.-X. Mo, X. Sui, Generalized s-convex functions on fractal sets, Abstr. Appl. Anal., 2014 (2014), 1-8
##[9]
H.-X. Mo, X. Sui, Hermite-Hadamard-type inequalities for generalized s-convex functions on real linear fractal set \(\mathbb{R}^\alpha (0 < \alpha < 1)\), Math. Sci. (Springer), 11 (2017), 241-246
##[10]
H.-X. Mo, X. Sui, D.-Y. Yu, Generalized convex functions on fractal sets and two related inequalities, Abstr. Appl. Anal., 2014 (2014), 1-7
##[11]
S. K. Ntouyas, P. Agarwal, J. Tariboon, On Pólya-Szegő and Chebyshev types inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal., 10 (2016), 491-504
##[12]
M. Z. Sarikaya, H. Budak, Generalized Ostrowski type inequalities for local fractional integrals, Proc. Amer. Math. Soc., 145 (2017), 1527-1538
##[13]
M. Z. Sarikaya, S. Erden, H. Budak, Some generalized Ostrowski type inequalities involving local fractional integrals and applications, RGMIA Research Report Collection, 18 (2015), 1-12
##[14]
M. Z. Sarikaya, T. Tunc, H. Budak, On generalized some integral inequalities for local fractional integrals, Appl. Math. Comput., 276 ( 2016), 316-323
##[15]
E. Set, M. Tomar, New inequalities of Hermite-Hadamard type for generalized convex functions with applications, Facta Univ. Ser. Math. Inform., 31 (2016), 383-397
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H. M. Srivastava, J.-S. Choi , Zeta and q-Zeta functions and associated series and integrals, Elsevier, Inc., Amsterdam (2012)
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X.-J. Yang, Generalized local fractional Taylor’s formula with local fractional derivative, ArXiv, 2011 (2011), 1-5
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X.-J. Yang , Local fractional functional analysis and its applications, Asian Academic publisher Limited, Hong Kong (2011)
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X.-J. Yang , Advanced local fractional calculus and its applications, World Science Publisher, New York (2012)
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X.-J. Yang , Local fractional Fourier analysis, Adv. Mech. Eng. Appl., 1 (2012), 12-16
##[21]
X.-J. Yang, Local fractional integral equations and their applications, Adv. Comput. Sci. Appl., 1 (2012), 234-239
##[22]
Y.-J. Yang, D. Baleanu, X.-J. Yang, Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys., 2013 (2013), 1-6
]
Expected residual minimization method for uncertain variational inequality problems
Expected residual minimization method for uncertain variational inequality problems
en
en
This paper considers an uncertain variational inequality problem (UVIP).
We first establish UVIP as an optimization problem (ERM model) which minimizes
the expected residual of the so-called regularized gap function. Then, we make some assumptions about a
UVIP subclass in which the function involved is affine. Thus the priority in our paper is to discuss the properties of the ERM problem and comprehensive convergence analysis under uncertainty theory. In the end, we make a conclusion.
5958
5975
Cunlin
Li
School of Management
North Minzu University
China
bitlcl@163.com
Zhifu
Jia
School of Mathematics and Information Science
North Minzu University
China
2451343541@qq.com
Lin
Zhang
School of Mathematics and Information Science
North Minzu University
China
bitlcl@163.com
Uncertain variational inequalities
uncertainty theory
properties of the ERM problem
convergence
Article.33.pdf
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[1]
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Q.-Q. Chen, Y.-G. Zhu, A class of uncertain variational inequality problems, J. Inequal Appl., 2015 (2015), 1-13
##[4]
F. Facchinei, J.-S. Pang , Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York (2003)
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B. Liu, Uncertainty Theory, Springer-Verlag, Berlin (2007)
##[9]
B. Liu , Uncertainty Theory , Springer-Verlag, Berlin (2015)
##[10]
Y.-H. Yao, M. Postolache, Y.-C. Liou, Z.-S. Yao, Construction algorithms for a class of monotone variational inequalities, Optim. Lett., 10 (2016), 1519-1528
##[11]
Y.-H. Yao, X. Qin, J.-C. Yao, An improved algorithm based on Korpelevich’s method for variational inequalities in Banach spaces, J. Nonlinear Convex Anal., (in press), -
##[12]
Y.-H. Yao, N. Shahzad, Strong convergence of a proximal point algorithm with general errors, Optim. Lett., 6 (2012), 621-628
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Y.-H. Yao, N. Shahzad , An algorithmic approach to the split variational inequality and fixed point problem, J. Nonlinear Convex Anal., 18 (2017), 977-991
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H. Zegeye, N. Shahzad, Y.-H. Yao, Minimum-norm solution of variational inequality and fixed point problem in Banach spaces, Optimization, 64 (2015), 453-471
]
Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system
Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system
en
en
Ultimate bound sets of chaotic systems have important applications in chaos control and chaos synchronization. Ultimate bound sets can also be applied in estimating the dimensions of chaotic attractors. However, it is often a difficult work to obtain the bounds of high-order chaotic systems due to complex algebraic structure of high-order chaotic systems. In this paper, a new 5D autonomous quadratic chaotic system which is different from the Lorenz chaotic system is proposed and analyzed. Ultimate bound sets and globally exponential attractive sets of this system are studied by introducing the Lyapunov-like functions. To validate the ultimate bound estimation, numerical simulations are also investigated.
5976
5984
Fuchen
Zhang
College of Mathematics and Statistics
Mathematical Postdoctoral station, College of Mathematics and Statistics
Chongqing Technology and Business University
Southwest University
People's Republic of China
People’s Republic of China
zhangfuchen1983@163.com
Xiaofeng
Liao
College of Electronic and Information Engineering
Southwest University
People's Republic of China
xuekectbu123@163.com
Chunlai
Mu
College of Mathematics and Statistics
Chongqing University
People's Republic of China
315683955@qq.com
Guangyun
Zhang
College of Mathematics and Statistics
Chongqing Technology and Business University
People's Republic of China
bihaihongyun@163.com
Xiaomin
Li
College of Mathematics and Statistics
Chongqing Technology and Business University
People's Republic of China
65328356@qq.com
Lorenz-type system
Lyapunov exponents
Lyapunov stability
chaotic attractor
ultimate bound estimation
Article.34.pdf
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F.-C. Zhang, X.-F. Liao, C.-L. Mu, G.-Y. Zhang, Y.-A. Chen, On global boundedness of the Chen system , Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 1673-1681
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F.-C. Zhang, X.-F. Liao, G.-Y. Zhang, On the global boundedness of the Lü system, Appl. Math. Comput., 284 (2016), 332-339
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F.-C. Zhang, X.-F. Liao, G.-Y. Zhang, Qualitative behaviors of the continuous-time chaotic dynamical systems describing the interaction of waves in plasma, Nonlinear Dyn., 88 (2017), 1623-1629
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F.-C. Zhang, X.-F. Liao, G.-Y. Zhang, C.-L. Mu, Dynamical analysis of the generalized Lorenz systems, J. Dyn. Control Syst., 23 (2017), 349-362
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F.-C. Zhang, C.-L. Mu, S.-M. Zhou, P. Zheng, New results of the ultimate bound on the trajectories of the family of the Lorenz systems, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 1261-1276
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F.-C. Zhang, G.-Y. Zhang, Further results on ultimate bound on the trajectories of the Lorenz system, Qual. Theory Dyn. Syst., 15 (2016), 221-235
]
Almost sure exponential stability for time-changed stochastic differential equations
Almost sure exponential stability for time-changed stochastic differential equations
en
en
Some sufficient conditions for almost sure exponential stability of solutions to time-changed stochastic differential equations (SDEs) are presented.
The principle technique of our investigation is to construct a proper Lyapunov function and carry out generalized Lyapunov methods to time-changed SDEs. In contrast to the almost sure exponential stability in existing articles, we present new results on the stability of solutions to time-changed SDEs. Finally, an example is given to demonstrate the effectiveness of our work.
5985
5998
Yongxiang
Zhu
College of Traffic Engineering
Hunan University of Technology
China
zyx1998@sina.com
Min
Zhu
College of Traffic Engineering
School of Mathematics and Statistics
Hunan University of Technology
Central South University
China
China
zhumin0107@csu.edu.cn
Junping
Li
School of Mathematics and Statistics
Central South University
China
jpli@mail.csu.edu.cn
Time-changed stochastic differential equations
almost sure exponential stability
time-changed Brownian motion
Article.35.pdf
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[1]
J.-H. Bao, Z.-T. Hou, C.-G. Yuan, Stability in distribution of mild solutions to stochastic partial differential equations, Proc. Amer. Math. Soc., 138 (2010), 2169-2180
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J.-H. Bao, A. Truman, C.-G. Yuan, Almost sure asymptotic stability of stochastic partial differential equations with jumps, SIAM J. Control Optim., 49 (2011), 771-787
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P. Carra, L.-R. Wu, Time-changed Lévy processes and option pricing, J. Financial Econ., 71 (2004), 113-141
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Q.-X. Zhu, Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise, J. Math. Anal. Appl., 416 (2014), 126-142
]
On a completely non-unitary contraction and associated dissipative difference operator
On a completely non-unitary contraction and associated dissipative difference operator
en
en
In this paper, we investigate the spectral properties of dissipative
difference operator, dissipative sum operator and contractive
operator. Using Solomyak's method, we construct the characteristic
function of the dissipative difference operator. For this purpose,
we use boundary spaces and functional embeddings. Then we pass to
the characteristic function of the Cayley transform of the
dissipative difference operator which is a completely non-unitary
contraction belonging to the class \(C_{0}\). With the aid of this
characteristic function we achieve to pass to the minimal function
of the contraction and we investigate the complete spectral analysis
of both the contractive and dissipative operators. Embedding the
associated contraction to its natural unitary colligation, we obtain a Carathéodory function. Moreover, self-adjoint dilation of the maximal
dissipative difference operator and its incoming and outgoing
eigenfunctions are constructed. Finally, the truncated CMV matrix is
established which is unitary equivalent to the contractive operator.
5999
6019
Ekin
Uğurlu
Cankaya University, Faculty of Arts and Science
Department of Mathematics
Turkey
ekinugurlu@cankaya.edu.tr
Dumitru
Baleanu
Cankaya University, Faculty of Arts and Science
Institute of Space Sciences
Department of Mathematics
Turkey
Romania
dumitru@cankaya.edu.tr
Difference operator
completely non-unitary contraction
dissipative operator
characteristic function
CMV matrix
Article.36.pdf
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]
Infinitely many solutions for a class of p-Laplacian equation with Sturm-Liouville type nonhomogeneous boundary conditions
Infinitely many solutions for a class of p-Laplacian equation with Sturm-Liouville type nonhomogeneous boundary conditions
en
en
We establish the criteria for the existence of infinitely many solutions for a class of one-dimensional p-Laplacian equations with Sturm-Liouville type nonhomogeneous boundary conditions. The nonlinear term has two parameters \(\lambda,\,\mu\) and is dependent on \(x\) and the derivative \(u'(x)\) of the solution to be determined. The main method used for the study is Ricceri's Variational Principle.
6020
6034
Fenglong
Sun
School of Mathematical Sciences
Qufu Normal University
People’s Republic of China
sfenglong@sina.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
People’s Republic of China
Australia
mathlls@163.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
Y.Wu@curtin.edu.au
Infinitely many solutions
p-Laplacian equation
nonhomogeneous boundary conditions
variational method
Article.37.pdf
[
[1]
G. A. Afrouzi, G. Caristi, D. Barilla, S. Moradi, A variational approach to perturbed three-point boundary value problems of Kirchhoff-type, Complex Var. Elliptic Equ., 62 (2017), 397-412
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D. Averna, G. Bonanno, Three solutions for a quasilinear two-point boundary value problem involving the one-dimensional p-Laplacian, Proc. Edinb. Math. Soc., 47 (2004), 257-270
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G. Barletta, A. Chinnì, D. O’Regan, Existence results for a Neumann problem involving the p(x)-Laplacian with discontinuous nonlinearities, Nonlinear Anal. Real World Appl., 27 (2016), 312-325
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G. Bonanno , Multiple critical points theorems without the Palais-Smale condition, J. Math. Anal. Appl., 299 (2004), 600-614
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G. Bonanno, P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059
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G. Bonanno, B. Di Bella, J. Henderson, Infinitely many solutions for a boundary value problem with impulsive effects, Bound. Value Probl., 2013 (2013), 1-14
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G. Bonanno, N. Giovannelli, An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities, J. Math. Anal. Appl., 308 (2005), 596-604
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G. Bonanno, P. Jebelean, C. Şerban, Superlinear discrete problems , Appl. Math. Lett., 52 (2016), 162-168
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G. Bonanno, G. Molica Bisci, V. Rădulescu , Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems, Nonlinear Anal. Real World Appl., 12 (2011), 2656-2665
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H. Brezis , Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York (2011)
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H. Chen, J. Sun, An application of variational method to second-order impulsive differential equation on the half-line, Appl. Math. Comput., 217 (2010), 1863-1869
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J.-F. Chu, F. Gharehgazlouei, S. Heidarkhani, A. Solimaninia, Three nontrivial solutions for Kirchhoff-type variational-hemivariational inequalities, Results Math., 68 (2015), 71-91
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G. D'Aguì, J. Mawhin, A. Sciammetta , Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian, J. Math. Anal. Appl., 447 (2017), 383-397
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G. D'Aguì, A. Sciammetta, Infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous Neumann conditions, Nonlinear Anal., 75 (2012), 5612-5619
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G. Dai , Three solutions for a nonlocal dirichlet boundary value problem involving the p(x)-Laplacian, Appl. Anal., 92 (2013), 191-210
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F. Faraci, G. Smyrlis, Three solutions for a class of higher dimensional singular problems, NoDEA Nonlinear Differential Equations Appl., 2016 (2016), 1-14
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J. R. Graef, S. Heidarkhani, L.-J. Kong , Infinitely many solutions for systems of Sturm-Liouville boundary value problems , Results Math., 66 (2014), 327-341
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S. Heidarkhani, G. A. Afrouzi, M. Ferrara, S. Moradi, Variational approaches to impulsive elastic beam equations of Kirchhoff type, Complex Var. Elliptic Equ., 61 (2016), 931-968
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S. Heidarkhani, M. Ferrara, S. Khademloo , Nontrivial solutions for one-dimensional fourth-order Kirchhoff-type equations, Mediterr. J. Math., 13 (2016), 217-236
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. Liu, Z. Zhao , Multiple solutions for impulsive problems with non-autonomous perturbations, Appl. Math. Lett., 64 (2017), 143-149
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S. A. Marano, D. Motreanu, On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems, Nonlinear Anal., 48 (2002), 37-52
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B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math., 113 (2000), 401-410
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B. Ricceri, On a three critical points theorem, Arch. Math. (Basel), 75 (2000), 220-226
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B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (2009), 3084-3089
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B. Ricceri , On an elliptic Kirchhoff-type problem depending on two parameters, J. Global Optim., 46 (2010), 543-549
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R. Rodríguez-López, S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal., 17 (2014), 1016-1038
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Y. Tian, W. Ge, Multiple solutions for a second-order Sturm-Liouville boundary value problem, Taiwanese J. Math., 11 (2007), 975-988
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Y. Tian, J. R. Graef, L. Kong, M. Wang , Three solutions for second-order impulsive differential inclusions with Sturm- Liouville boundary conditions via nonsmooth critical point theory, Topol. Methods Nonlinear Anal., 47 (2016), 1-17
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L. Yang, H. Chen, X.-X. Yang, The multiplicity of solutions for fourth-order equations generated from a boundary condition, Appl. Math. Lett., 24 (2011), 1599-1603
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E. Zeidler , Nonlinear Functional Analysis and Its Applications , Springer, New York (1988)
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X. Zhang, L. Liu, Y. Wu, B. Wiwatanapataphee, Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion, Appl. Math. Lett., 66 (2017), 1-8
]
Refinements of Hermite-Hadamard inequality for operator convex function
Refinements of Hermite-Hadamard inequality for operator convex function
en
en
In this paper, we present several operator versions of the Hermite-Hadamard inequality for the operator convex function, which are refinements of some operator convex inequalities presented by Dragomir [S. S. Dragomir, Appl. Math. Comput., \({\bf 218}\) (2011), 766--772] and [S. S. Dragomir, RGMIA Research Report Collection, \({\bf 2016}\) (2016), 15 pages].
6035
6041
Junmin
Han
School of Mathematics and Information Science
Weifang University
P. R. China
goodlucktotoro@126.com
Jian
Shi
College of Mathematics and Information Science
Hebei University
P. R. China
mathematic@126.com
Self-adjoint operators
Hermite-Hadamard inequality
operator convex functions
Article.38.pdf
[
[1]
V. Bacak, R. Türkmen, Refinements of Hermite-Hadamard type inequalities for operator convex functions, J. Inequal. Appl., 2013 (2013), 1-10
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N. S. Barnett, P. Cerone, S. S. Dragomir, Some new inequalities for Hermite-Hadamard divergence in information theory, Stochastic analysis and applications, Stoch. Anal. Appl., 3 (2002), 7-19
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A. Burqan , Improved Cauchy-Schwarz norm inequality for operators, J. Math. Inequal., 10 (2016), 205-211
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S. S. Dragomir, Hermite-Hadamard type inequalities for operator convex functions, Appl. Math. Comput., 218 (2011), 766-772
##[5]
S. S. Dragomir, Some Hermite-Hadamard Type Inequalities for Operator Convex Functions and Positive Maps, RGMIA Research Report Collection, 2016 (2016), 1-15
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S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities, RGMIA Monographs, Victoria University (2000)
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Y. Feng, Refinements of the Heinz inequalities, J. Inequal. Appl., 2012 (2012), 1-6
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A. G. Ghazanfari, A. Barani, Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions, Banach J. Math. Anal., 9 (2015), 9-20
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D. S. Mitrinović, I. B. Lacković, Hermite and convexity , Aequationes Math., 28 (1985), 229-232
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M. S. Moslehian, Matrix Hermite-Hadamard type inequalities, Houston J. Math., 39 (2013), 177-189
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C. P. Niculescu, L.-E. Persson, Convex functions and their applications: A contemporary approach, Springer, New York (2006)
]
Nontrivial solutions for a fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions
Nontrivial solutions for a fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions
en
en
The model of fractional differential equation arises from various fields of physics, engineering, and applied mathematics. In this paper,
we focus on the existence and uniqueness of nontrivial solutions for a abstract model of fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions. Under certain suitable growth conditions, we establish some sufficient conditions for the existence and uniqueness of nontrivial solutions based on Leray-Schauder nonlinear alternative and Schauder fixed point theorem.
6042
6055
Xinguang
Zhang
School of Mathematical and Informational Sciences
Department of Mathematics and Statistics
Yantai University
Curtin University of Technology
China
Australia
zxg123242@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University of Technology
China
Australia
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University of Technology
Australia
Yujun
Cui
Department of Mathematics
Shandong University of Science and Technology
China
Fractional differential equation
nontrivial solution
nonlocal Riemann-Stieltjes boundary conditions
fixed point theorem
Article.39.pdf
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[1]
A. Azar, S. Vaidyanathan, A. Ouannas, Fractional Order Control and Synchronization of Chaotic Systems, Springer- Verlag, Germany (2017)
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I. Podlubny, Fractional Differential Equations , Mathematics in Science and Engineering, Academic Press, New York (1999)
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T. Ren, S. Li, X.-G. Zhang, Positive solutions of a weakly singular periodic eco-economic system with changing-sign perturbation, J. Nonlinear Sci. Appl., 10 (2017), 2539-2549
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T. Ren, S. Li, X.-G. Zhang, L. Liu, Maximum and minimum solutions for a nonlocal p-Laplacian fractional differentialsystem from eco-economical processes, Bound. Value Probl., 2017 (2017), 1-15
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F.-L. Sun, L. Liu, X.-G. Zhang, Y.-H. Wu, Spectral analysis for a singular differential system with integral boundary conditions, Mediterr. J. Math., 13 (2016), 4763-4782
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X.-J. Yang, Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems, Therm. Sci., 21 (2017), 1161-1171
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X.-J. Yang, J. A. Machado, D. Baleanu, Anomalous diffusion models with general fractional derivatives within the kernels of the extended Mittag-Leffler type functions, Rom. Rep. Phys., 2017 (2017), 1-19
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X.-J. Yang, H. M. Srivastava, J. A. Tenreiro Machadod , A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow, Therm. Sci., 20 (2017), 753-756
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X.-G. Zhang, Y.-F. Han, Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations, Appl. Math. Lett., 25 (2012), 555-560
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X.-G. Zhang, L. Liu, B. Wiwatanapataphee, Y.-H. Wu, Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives, Abstr. Appl. Anal., 2012 (2012), 1-16
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X.-G. Zhang, L. Liu, B. Wiwatanapataphee, Y.-H. Wu, The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition, Appl. Math. Comput., 235 (2014), 412-422
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X.-G. Zhang, L. Liu, Y.-H. Wu, Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives, Appl. Math. Comput., 219 (2012), 1420-1433
##[29]
X.-G. Zhang, L. Liu, Y.-H. Wu, The eigenvalue problem for a singular higher fractional differential equation involving fractional derivatives, Appl. Math. Comput., 218 (2012), 8526-8536
##[30]
X.-G. Zhang, L. Liu, Y.-H. Wu, The uniqueness of positive solution for a singular fractional differential system involving derivatives, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1400-1409
##[31]
X.-G. Zhang, L. Liu, Y.-H. Wu, The uniqueness of positive solution for a fractional order model of turbulent flow in a porous medium , Appl. Math. Lett., 37 (2014), 26-33
##[32]
X.-G. Zhang, L. Liu, Y.-H. Wu , Variational structure and multiple solutions for a fractional advection-dispersion equation, Comput. Math. Appl., 68 (2014), 1794-1805
##[33]
X.-G. Zhang, L. Liu, Y.-H. Wu, B. Wiwatanapataphee , The spectral analysis for a singular fractional differential equation with a signed measure, Appl. Math. Comput., 257 (2015), 252-263
##[34]
X.-G. Zhang, L. Liu, Y.-H. Wu, B. Wiwatanapataphee, Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion, Appl. Math. Lett., 66 (2017), 1-8
##[35]
X.-G. Zhang, C. Mao, L. Liu, Y.-H. Wu, Exact iterative solution for an abstract fractional dynamic system model for Bioprocess , Qual. Theory Dyn. Syst., 16 (2017), 205-222
##[36]
X.-G. Zhang, Y.-H. Wu, L. Caccetta , Nonlocal fractional order differential equations with changing-sign singular perturbation, Appl. Math. Model., 39 (2015), 6543-6552
]
Existence and multiplicity of positive solutions for a nonlocal problem
Existence and multiplicity of positive solutions for a nonlocal problem
en
en
In this work, we are interested in considering the following nonlocal problem
\[
\begin{cases}
-\left(a-b\displaystyle\int_{\Omega}|\nabla u|^2dx\right)\Delta u= f(x)|u|^{p-2}u,
\quad\text{in }\Omega, \\
u=0, \quad\text{on }\partial\Omega,
\end{cases}
\]
where \(\Omega\subset\mathbb{R}^{N}~(N\geq3)\) is a bounded domain with smooth boundary \(\partial\Omega, a,b>0, 1\leq p<2^*\),
\(f\in L^{\frac{2^*}{2^{*}-p}}(\Omega)\) is nonzero and nonnegative. By using the variational method, some existence and multiplicity results are obtained.
6056
6061
Yu
Duan
College of Science
Guizhou University of Engineering Science
People's Republic of China
Xin
Sun
College of Science
Guizhou University of Engineering Science
People's Republic of China
Hong-Ying
Li
School of Mathematics and Information
China West Normal University
People's Republic of China
lihongyingnch@163.com
Nonlocal problem
positive solutions
variational method
Article.40.pdf
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C.-Y. Lei, C.-M. Chu, H.-M. Suo, Positive solutions for a nonlocal problem with singularity, Electron. J. Differential Equations, 2017 (2017), 1-9
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C.-Y. Lei, J.-F. Liao, H.-M. Suo , Multiple positive solutions for nonlocal problems involving a sign-changing potential , Electron. J. Differential Equations, 2017 (2017), 1-8
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T.-F. Wu , On semilinear elliptic equation involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl., 318 (2006), 253-270
##[5]
G.-S. Yin, J.-S. Liu, Existence and multiplicity of nontrivial solutions for a nonlocal problem, Bound. Value Probl., 2015 (2015), 1-7
]
Topological conjugacy of PM functions with height equaling \(\infty\)
Topological conjugacy of PM functions with height equaling \(\infty\)
en
en
It is known that topological conjugacy
is a basic equivalence relation in
dynamical systems.
In this paper we study a class of piecewise monotone and continuous functions
with infinite height. Those
functions are topologically conjugate with each other if and only if
they have same sequences describing itineraries of all forts, endpoints, and fixed points.
We construct the topological conjugacy by extension, which partly generalizes previous results.
6062
6070
Pingping
Zhang
Department of Mathematics
Binzhou University
P. R. China
ppz2005@163.com
Topological conjugacy
homeomorphism
piecewise monotone
fort
Article.41.pdf
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S. Baldwin , A complete classification of the piecewise monotone functions on the interval, Trans. Amer. Math. Soc., 319 (1990), 155-178
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Z. Leśniak, Y.-G. Shi, Topological conjugacy of piecewise monotonic functions of nonmonotonicity height \(\geq 1\), J. Math. Anal. Appl., 423 (2015), 1792-1803
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L. Li , A topological classification for piecewise monotone iterative roots, Aequationes Math., 91 (2017), 137-152
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D. Stowe, Linearization in two dimensions, J. Differential Equations, 63 (1986), 183-226
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W.-N. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math., 65 (1997), 119-128
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]
Analysis of a delayed SIR model subject to multiple infectious stages and nonlinear incidence rate
Analysis of a delayed SIR model subject to multiple infectious stages and nonlinear incidence rate
en
en
We investigate the threshold dynamics problem of a delayed Susceptible-Infected-Recovered (SIR) model with general nonlinear incidence and multiple parallel infectious stages. Biologically, the model contains the following aspects:
(i) once infection occurs, a fraction of the infected individuals is detected and treated, while the rest of the infected remains undetected and untreated;
(ii) distributed delays governed by a general nonlinear incidence function are included into the model due to the complexity of disease transmissions.
Mathematically, under some suitable assumptions on nonlinear incidence rate, we prove that the reproduction number \(\Re_0 \) can be used to govern the the global dynamics of the model. The proofs of global attractivity of disease-free equilibrium (which means the extinction of disease) and endemic equilibrium (which means the persistence of the disease) are achieved by constructing suitable Lyapunov functionals.
6071
6083
Hong
Zhang
School of Mathematical Science
Harbin Normal University
China
28812965@qq.com
Chunming
Li
School of Mathematical Science
Heilongjiang University
China
lichunming@hlju.edu.cn
Hongquan
Sun
School of Mathematical Science
Heilongjiang University
China
sunhongquan@hlju.edu.cn
SIR epidemic model
nonlinear incidence
global attractivity
Lyapunov functional
Article.42.pdf
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[1]
V. Capasso, G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci., 42 (1978), 43-61
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K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain J. Math., 9 (1979), 31-42
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##[11]
A. Korobeinikov, P. K. Maini, Nonlinear incidence and stability of infectious disease models, Math. Med. Biol., 22 (2005), 113-128
##[12]
C. C. McCluskey , Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), 603-610
##[13]
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. Real World Appl., 11 (2010), 55-69
##[14]
C. C. McCluskey, Global stability for an SIR epidemic model with delay and nonlinear incidence, Nonlinear Anal. Real World Appl., 11 (2010), 3106-3109
##[15]
C. C. McCluskey, Global stability of an SIR epidemic model with delay and general nonlinear incidence, Math. Biosci. Eng., 7 (2010), 837-850
##[16]
Z. Shuai, P. van en Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math., 73 (2013), 1513-1532
##[17]
X. Wang, S. Liu, Global properties of a delayed SIR epidemic model with multiple parallel infectious stages, Math. Biosci. Eng., 9 (2012), 685-695
##[18]
R. Xu, Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. Real World Appl., 10 (2009), 3175-3189
]
Fixed points for multivalued contractions with respect to a Pompeiu type metric
Fixed points for multivalued contractions with respect to a Pompeiu type metric
en
en
The purpose of this paper is to present a fixed point theory for multivalued \(H^+\)-contractions from
the following perspectives: existence/uniqueness of the fixed and strict fixed points, data dependence of the fixed point set,
sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property for a multivalued operator, set-to-set operatorial equations and fractal operator theory.
6084
6101
Iulia
Coroian
Department of Land Measurements and Exact Sciences
University Of Agricultural Sciences and Veterinary Medicine
Romania
coroian.iulia@gmail.com
\(H^{+}\)-type multivalued mapping
Lipschitz equivalent metric
multivalued operator
contraction
Article.43.pdf
[
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A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem
A mass-conservative characteristic splitting mixed element method for saltwater intrusion problem
en
en
A new characteristic mixed finite element method is developed for solving saltwater intrusion problem. In this algorithm, the splitting mixed finite element (SMFE) method is applied for solving the parabolic-type water head equation, and the mass-conservative characteristic (MCC) finite element method is applied for solving the convection-diffusion type concentration equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the mixed element system and separating the flux equation from the water head equation. While the mass-conservative characteristic finite element method does well in handling convection-dominant diffusion problem and keeps mass balance. The convergence of this method is considered and the optimal \(L^2\)-norm error estimate is also derived.
6102
6118
Jiansong
Zhang
Department of Applied Mathematics
China University of Petroleum
China
jszhang@upc.edu.cn
Yuezhi
Zhang
Department of Applied Mathematics
China University of Petroleum
China
zhangyuezhi2015@163.com
Zhaohui
Liu
Department of Applied Mathematics
China University of Petroleum
China
liuzhaohui2016@163.com
Method of characteristics
mass-conservative
splitting mixed finite element
error estimate
saltwater intrusion problem
Article.44.pdf
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]
Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales
Anti-periodic solutions for neutral type FCNNs with time-varying delays and \(D\) operator on time scales
en
en
In this paper, we consider a class of neutral type fuzzy cellular neural networks with time-varying delays and \(D\) operator on time scales. Based on inequality analysis techniques on time scales and a fixed point theorem and the theory of calculus on time scales, we obtain the existence and global exponential stability of anti-periodic solutions for this class of the networks. Finally, a numerical example is given to illustrate the feasibility of our results.
6119
6131
Bing
Li
School of Mathematics and Computer Science
Yunnan Nationalities University
People's Republic of China
bli123@126.com
Yongkun
Li
Department of Mathematics
Yunnan University
People's Republic of China
yklie@ynu.edu.cn
Fuzzy cellular neural networks
anti-periodic solution
\(D\) operator
global exponential stability
time scales
Article.45.pdf
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]
Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity
Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity
en
en
This paper mainly studies the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial variation: one lives in the heterogeneity environment, the other lives in the homogeneity environment. The main results of this paper are two fold: (i) The species living in homogeneous environment can never wipe out their competitor; (ii) Explore the condition on the diffusion and advection rates for exclusion and coexistence.
It is proved that for fixed dispersal rates, when the strength of the advection is sufficiently strong, the two competitive species coexist. This is a remarkable different result with that obtained by He and Ni recently for
corresponding systems without advection [X. He, W.-M. Ni, J. Differential Equations, \({\bf254}\) (2013), 528--546].
6132
6140
Benlong
Xu
Department of Mathematics
Shanghai Normal University
P. R. China
bxu@shnu.edu.cn
Hongyan
Jiang
Department of Mathematics
Shanghai Normal University
P. R. China
961089322@qq.com
Advection
linear stability
global asymptotic stability
spatial heterogeneity
coexistence
Article.46.pdf
[
[1]
I. Averill, K.-Y. Lam, Y. Lou , The role of advection in a two-species competition model: a bifurcation approach, American Mathematical Society, New York (2017)
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Y. Lou , On the effects of migration and spatial heterogeneity on single and multiple species, J. Differential Equations, 223 (2006), 400-426
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]