International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171222An existence theorem on Hamiltonian \((g,f)\)-factors in networks17http://dx.doi.org/10.22436/jnsa.011.01.01ENSizhong ZhouSchool of Science, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, P. R. ChinaLet \(a,b\), and \(r\) be nonnegative integers with
\(\max\{3,r+1\}\leq a<b-r\), let \(G\) be a graph of order \(n\), and let \(g\) and
\(f\) be two integer-valued functions defined on \(V(G)\) with
\(\max\{3,r+1\}\leq a\leq g(x)<f(x)-r\leq b-r\) for any \(x\in V(G)\).
In this article, it is proved that if
\(n\geq\frac{(a+b-3)(a+b-5)+1}{a-1+r}\) and
\({\rm bind}(G)\geq\frac{(a+b-3)(n-1)}{(a-1+r)n-(a+b-3)}\), then \(G\)
admits a Hamiltonian \((g,f)\)-factor.http://www.isr-publications.com/jnsa/6507/download-an-existence-theorem-on-hamiltonian-gf-factors-in-networksInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171222Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems816http://dx.doi.org/10.22436/jnsa.011.01.02ENQiao-Luan LiCollege of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, ChinaWing-Sum CheungDepartment of Mathematics, The University of Hong Kong, Hong Kong, ChinaIn this paper, we establish some new
Lyapunov-type inequalities for a class of Laplacian systems.
With these, sufficient conditions for the non-existence of nontrivial solutions to certain
boundary value problems are obtained. A lower bound for the eigenvalues is also deduced. http://www.isr-publications.com/jnsa/6508/download-lyapunov-type-inequalities-for-laplacian-systems-and-applications-to-boundary-value-problemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171222Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term1725http://dx.doi.org/10.22436/jnsa.011.01.03ENShuipingYangSchool of Mathematics and Big Data Science, Huizhou University, Guangdong, 516007, ChinaIn this paper, we propose a finite difference method for the Riesz space fractional diffusion equations with delay and a nonlinear source term on a finite domain.
The proposed method combines a time scheme based on the predictor-corrector method and the Crank-Nicolson scheme for the spatial discretization.
The corresponding theoretical results including stability and convergence are provided. Some numerical examples are presented to validate the proposed method.http://www.isr-publications.com/jnsa/6509/download-finite-difference-method-for-riesz-space-fractional-diffusion-equations-with-delay-and-a-nonlinear-source-termInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171222Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces2648http://dx.doi.org/10.22436/jnsa.011.01.04ENXiaoli ChenDepartment of Mathematics, Jiangxi Normal University Nanchang, Jiangxi 330022, P. R. China In this paper, we obtain bounded criteria on certain
weighted Morrey spaces for the commutators generalized by some sublinear
integral operators and weighted Lipschitz functions. We also present bounded
criteria for commutators generalized by such sublinear integral operators
and weighted BMO function on the weighted Morrey spaces. As applications, our
results yield the same bounded criteria for those commutators on the
classical weighted Morrey spaces.http://www.isr-publications.com/jnsa/6510/download-boundedness-criteria-for-commutators-of-some-sublinear-operators-in-weighted-morrey-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171224On some rational systems of difference equations4972http://dx.doi.org/10.22436/jnsa.011.01.05ENM. M. El-DessokyMathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaA.KhaliqDepartment of Mathematics, Riphah International University, Lahore, PakistanA.AsiriMathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaOur goal in this paper is to find the form of solutions for the following
systems of rational difference equations:
\[
x_{n+1}=\frac{x_{n-3}y_{n-4}}{y_{n}(\pm 1\pm x_{n-3}y_{n-4})},\quad
y_{n+1}=\frac{y_{n-3}x_{n-4}}{x_{n}(\pm 1\pm y_{n-3}x_{n-4})},\quad n=0,1,\ldots,
\]
where the initial conditions have non-zero real numbers. http://www.isr-publications.com/jnsa/6517/download-on-some-rational-systems-of-difference-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171224Common fixed points of monotone Lipschitzian semigroups in Banach spaces7379http://dx.doi.org/10.22436/jnsa.011.01.06ENM. BacharDepartment of Mathematics, College of Science, King Saud University, Saudi ArabiaMohamed A. KhamsiDepartment of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, U.S.A.W. M. KozlowskiSchool of Mathematics and Statistics, University of New South Wales, AustraliaM. BounkhelDepartment of Mathematics, College of Science, King Saud University, Saudi ArabiaIn this paper, we investigate the existence of common fixed points of monotone Lipschitzian semigroup in Banach spaces under the natural condition that the images under the action of the semigroup at certain point are comparable to the point. In particular, we prove that if one map in the semigroup is a monotone contraction mapping, then such common fixed point exists. In the case of monotone nonexpansive semigroup we prove the existence of common fixed points if the Banach space is uniformly convex in every direction. This assumption is weaker than uniform convexity.http://www.isr-publications.com/jnsa/6518/download-common-fixed-points-of-monotone-lipschitzian-semigroups-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171224On the rational difference equation \(y_{{n+1}}={\frac {\alpha_{{0}}y_{{n}}+\alpha_{{1}}y_{{n-p}}+\alpha_{{2}}y_{{n-q}} +\alpha_{{3}}y_{{n-r}}+\alpha_{{4}}y_{{n-s}}}{\beta_{{0}}y_{{n}}+\beta_{{1}}y_{{n-p} }+\beta_{{2}}y_{{n-q}}+\beta_{{3}}y_{{n-r}}+\beta_{{4}}y_{{n-s}}}}\)8097http://dx.doi.org/10.22436/jnsa.011.01.07ENA. M. AlotaibiSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, MalaysiaM. A. El-MoneamMathematics Department, Faculty of Science, Jazan University, Kingdom of Saudi ArabiaM. S. M. NooraniSchool of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, MalaysiaIn this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of
the rational difference equation
\[
y_{{n+1}
}={\frac {\alpha_{{0}}y_{{n}}+\alpha_{{1}}y_{{n-p}}+\alpha_{{2}}y_{{n-q}} +\alpha_{{3}}y_{{
n-r}}+\alpha_{{4}}y_{{n-s}}}{\beta_{{0}}y_{{n}}+\beta_{{1}}y_{{n-p} }+\beta_{{2}}y_{{n-q}
}+\beta_{{3}}y_{{n-r}}+\beta_{{4}}y_{{n-s}}}},
\]
where the coefficients \({\alpha_{i},\beta_{i}\in (0,\infty ),\
i=0,1,2,3,4},\) and \(p,q,r\), and \(s\) are positive integers. The initial
conditions \(y_{-s},...,y_{-r},..., y_{-q},..., y_{{-p }},...,
y_{-1},y_{0}\) are arbitrary positive real numbers such that \(p<q<r<s\).
Some numerical examples will be given to illustrate our result.http://www.isr-publications.com/jnsa/6519/download-on-the-rational-difference-equation-y-n1frac-alpha-0y-nalpha-1y-n-palpha-2y-n-q-alpha-3y-n-ralpha-4y-n-sbeta-0y-nbeta-1y-n-p-beta-2y-n-qbeta-3y-n-rbeta-4y-n-sInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171227Fixed point theorems for contractions of rational type in complete metric spaces98107http://dx.doi.org/10.22436/jnsa.011.01.08ENTomonari SuzukiDepartment of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, JapanSamet et al. in
[S. Samet, C. Vetro, H. Yazidi, J. Nonlinear Sci. Appl., \({\bf 6}\) (2013), 162--169]
proved some fixed point theorem for
contractions of rational type.
In order to clarify the mathematical structure of
contractions of rational type,
we generalize this theorem in a general setting.http://www.isr-publications.com/jnsa/6534/download-fixed-point-theorems-for-contractions-of-rational-type-in-complete-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120171231Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application108130http://dx.doi.org/10.22436/jnsa.011.01.09ENJingling ZhangDepartment of Mathematics, Tianjin University, Tianjin 300350, P. R. ChinaRavi P. AgarwalDepartment of Mathematics, Texas A \(\&\) M University-Kingsville, Texas 78363, USA.Nan JiangDepartment of Mathematics, Tianjin University, Tianjin 300350, P. R. ChinaThe purpose of this paper is to introduce and consider a new
accelerated hybrid shrinking projection method for finding a
common element of the set \(EP \cap F\) in reflexive Banach spaces,
where \(EP\) is the set of all solutions of a generalized equilibrium problem,
and \(F\) is the common fixed point set of finite uniformly closed families of
countable Bregman quasi-Lipschitz mappings.
It is proved that the sequence generated by the accelerated
hybrid shrinking projection iteration, converges strongly to the
point in \(EP \cap F,\) under some conditions. This result is also
applied to find the fixed point of Bregman asymptotically
quasi-nonexpansive mappings.
It is worth mentioning that, there are multiple projection
points from the multiple points in the projection algorithm.
Therefore the new projection method in this paper can accelerate the convergence
speed of iterative sequence. The new results improve and extend
the previously known ones in the literature.
http://www.isr-publications.com/jnsa/6565/download-accelerated-hybrid-iterative-algorithm-for-common-fixed-points-of-a-finite-families-of-countable-bregman-quasi-lipschitz-mappings-and-solutions-of-generalized-equilibrium-problem-with-applicationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120180112Quadruple random common fixed point results of generalized Lipschitz mappings in cone \(b\)-metric spaces over Banach algebras131149http://dx.doi.org/10.22436/jnsa.011.01.10ENChayut KongbanKMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandPoom KumamKMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandIn this paper, we introduce the concept of cone \(b\)-metric spaces over Banach algebras and present some quadruple random coincidence points and quadruple random common fixed point theorems for nonlinear operators in such spaces.
http://www.isr-publications.com/jnsa/6642/download-quadruple-random-common-fixed-point-results-of-generalized-lipschitz-mappings-in-cone-b-metric-spaces-over-banach-algebrasInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120180120Optimal inequalities for a Toader-type mean by quadratic and contraharmonic means150160http://dx.doi.org/10.22436/jnsa.011.01.11ENZhengchao JiCenter of Mathematical Sciences, Zhejiang University, Hangzhou 310027, ChinaQing DingCollege of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha 410205, ChinaTiehong ZhaoDepartment of Mathematics, Hangzhou Normal University, Hangzhou 311121, ChinaIn this paper, we present the best possible parameters \(\alpha_i, \beta_i\ (i=1,2,3)\) and \(\alpha_4,\beta_4\in(1/2,1)\) such that the double inequalities
\[\alpha_1Q(a,b)+(1-\alpha_1)C(a,b) <T_{Q,C}(a,b)<\beta_1Q(a,b)+(1-\beta_1)C(a,b),\]
\[\qquad\ Q^{\alpha_2}(a,b)C^{1-\alpha_2}(a,b) <T_{Q,C}(a,b)<Q^{\beta_2}(a,b)C^{1-\beta_2}(a,b),\]
\[\frac{Q(a,b)C(a,b)}{\alpha_3Q(a,b)+(1-\alpha_3)C(a,b)} <T_{Q,C}(a,b)<\frac{Q(a,b)C(a,b)}{\beta_3Q(a,b)+(1-\beta_3)C(a,b)},\]
\[C\left(\sqrt{\alpha_4a^2+(1-\alpha_4)b^2},\sqrt{(1-\alpha_4)a^2+\alpha_4b^2}\right) <T_{Q,C}(a,b)<C\left(\sqrt{\beta_4a^2+(1-\beta_4)b^2},\sqrt{(1-\beta_4)a^2+\beta_4b^2}\right)
\]
hold for all \(a, b>0\) with \(a\neq b\), where \(Q(a,b)\), \(C(a,b)\), and \(T(a,b)\) are the quadratic, contraharmonic, and Toader means, respectively, and \(T_{Q,C}(a,b)=T[Q(a,b),C(a,b)]\). As consequences, we provide new bounds for the complete elliptic integral of the second kind.http://www.isr-publications.com/jnsa/6666/download-optimal-inequalities-for-a-toader-type-mean-by-quadratic-and-contraharmonic-meansInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111120180120The fuzzy \(C\)-delta integral on time scales161171http://dx.doi.org/10.22436/jnsa.011.01.12ENXuexiao YouCollege of Computer and Information, Hohai University, Nanjing, Jiangsu 210098, P. R. ChinaDafang ZhaoSchool of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, P. R. ChinaJian ChengSchool of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, P. R. ChinaTongxing LiLinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. ChinaIn this paper, we introduce and study the \(C\)-delta integral of interval-valued functions and fuzzy-valued functions on time scales. Also, some basic properties of the fuzzy \(C\)-delta integral are proved. Finally, we give two necessary and sufficient conditions of integrability.http://www.isr-publications.com/jnsa/6667/download-the-fuzzy-c-delta-integral-on-time-scales