International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823A general implicit iteration for finding fixed points of nonexpansive mappings51575168http://dx.doi.org/10.22436/jnsa.009.08.01END. R.SahuDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India.Shin MinKangCenter for General Education, China Medical University, Taichung 40402, Taiwan.AjeetKumarDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India.Sun YoungChoDepartment of Mathematics, Gyeongsang National University, Jinju 52828, Korea.The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive
mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points
of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. The strong
convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the
sequence of parameters. Our results extend and improve the results given by Ke and Ma [Y. Ke, C. Ma,
Fixed Point Theory Appl., 2015 (2015), 21 pages], Xu et al. [H. K. Xu, M. A. Alghamdi, N. Shahzad, Fixed
Point Theory Appl., 2015 (2015), 12 pages], and many others.http://www.isr-publications.com/jnsa/2826/download-a-general-implicit-iteration-for-finding-fixed-points-of-nonexpansive-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823Variational principle for a three-point boundary value problem51695174http://dx.doi.org/10.22436/jnsa.009.08.02ENHong-YanLiuSchool of Fashion Technology, Zhongyuan University of Technology No. 41 Zhongyuan Road (M), 450007 Zhengzhou, China.Ji-HuanHeNational Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University 199 Ren-ai Road, 215123 Suzhou, China.Zhi-MinLiRieter (China) Textile Instrument Co., 1068 West Tianshan Road, 200335 Shanghai, China.A variational principle is established for a three-point boundary value problem. The stationary condition
includes not only the governing equation but also the natural boundary conditions. The paper reveals that
not every boundary condition adopts a variational formulation, and the existence and uniqueness of the
solutions of a three-point boundary value problem can be revealed by its variational formulation.http://www.isr-publications.com/jnsa/2827/download-variational-principle-for-a-three-point-boundary-value-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings51755188http://dx.doi.org/10.22436/jnsa.009.08.03ENYang-QingQiuDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.Jin-ZuoChenDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.Lu-ChuanCengDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.In this paper, by the strongly positive linear bounded operator technique, a new generalized Mann-type
hybrid composite extragradient CQ iterative algorithm is first constructed. Then by using the algorithm,
we find a common element of the set of solutions of the variational inequality problem for a monotone,
Lipschitz continuous mapping, the set of zeros of two families of finite maximal monotone mappings and
the set of fixed points of an asymptotically \(\kappa\)-strict pseudocontractive mappings in the intermediate sense
in a real Hilbert space. Finally, we prove the strong convergence of the iterative sequences, which extends
and improves the corresponding previous works.
http://www.isr-publications.com/jnsa/2828/download-strong-convergence-for-a-common-solution-of-variational-inequalities-fixed-point-problems-and-zeros-of-finite-maximal-monotone-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823Almost monotone contractions on weighted graphs51895195http://dx.doi.org/10.22436/jnsa.009.08.04ENMonther R.AlfuraidanDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals Dhahran 31261, Saudi Arabia.MostafaBacharDepartment of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia.Mohamed A.KhamsiDepartment of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA.Almost contraction mappings were introduced as an extension to the contraction mappings for which
the conclusion of the Banach contraction principle (BCP in short) holds. In this paper, the concept of
monotone almost contractions defined on a weighted graph is introduced. Then a fixed point theorem for
such mappings is given.
http://www.isr-publications.com/jnsa/2832/download-almost-monotone-contractions-on-weighted-graphsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823A study on a class of q-Euler polynomials under the symmetric group of degree n51965201http://dx.doi.org/10.22436/jnsa.009.08.05ENSerkanAraciDepartment of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey.UgurDuranDepartment of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey.MehmetAcikgozDepartment of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep, Turkey.Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J.
Nonlinear Sci. Appl., 9 (2016), 1077-1082], we study a class of q-Euler polynomials earlier given by Kim et
al. in [T. Kim, Y. H. Kim, K. W. Hwang, Proc. Jangjeon Math. Soc., 12 (2009), 77-92]. We derive some
new symmetric identities for q-extension of \(\lambda\)-Euler polynomials, using fermionic p-adic invariant integral
over the p-adic number field originally introduced by Kim in [T. Kim, Russ. J. Math. Phys., 16 (2009),
484-491], under symmetric group of degree n denoted by \(S_n\).
http://www.isr-publications.com/jnsa/2522/download-a-study-on-a-class-of-q-euler-polynomials-under-the-symmetric-group-of-degree-nInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823On best proximity points for various \(\alpha\)-proximal contractions on metric-like spaces52025218http://dx.doi.org/10.22436/jnsa.009.08.06ENHassenAydiUniversity of Dammam, Department of Mathematics, College of Education of Jubail, P. O. 12020, Industrial Jubail 31961, Saudi Arabia.AbdelbassetFelhiKing Faisal University, Department of Mathematics, College of Sciences, Al-Hassa, Saudi Arabia.We establish some best proximity points for various \(\alpha\)-proximal contractive non-self-mappings in the class
of metric-like spaces. We provide concrete examples. We also present some best proximity point theorems in
metric (metric-like) spaces endowed with a graph and in partially ordered metric spaces.
http://www.isr-publications.com/jnsa/2813/download-on-best-proximity-points-for-various-alpha-proximal-contractions-on-metric-like-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823On monotone mappings in modular function spaces52195228http://dx.doi.org/10.22436/jnsa.009.08.07ENButhinah A. BinDehaishDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21593, Saudi Arabia.Mohamed A.KhamsiDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.We prove the existence of fixed points of monotone \(\rho\)-nonexpansive mappings in \(\rho\)-uniformly convex
modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for
monotone mappings. We also discuss the validity of this result in modular function spaces where the
modular is uniformly convex in every direction. This property has never been considered in the context of
modular spaces.
http://www.isr-publications.com/jnsa/2719/download-on-monotone-mappings-in-modular-function-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160823Calculations on topological degrees of semi-closed 1-set-contractive operators in M-PN-spaces and applications52295237http://dx.doi.org/10.22436/jnsa.009.08.08ENJiandongYinDepartment of Mathematics, Nanchang University, Nanchang 330031, P. R. China.PinghuaYanDepartment of Mathematics, Nanchang University, Nanchang 330031, P. R. China.QianqianLengDepartment of Mathematics, Nanchang University, Nanchang 330031, P. R. China.The aim of the paper is to study some calculating problems of topological degrees of semi-closed 1-set-
contractive operators in M-PN-spaces. Under some weak and natural conditions, several calculation results
are obtained. Finally, in order to verify the validity of our results, a support example is given at the end of
the paper.
http://www.isr-publications.com/jnsa/2355/download-calculations-on-topological-degrees-of-semi-closed-1-set-contractive-operators-in-m-pn-spaces-and-applicationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830A multi-dimensional functional equation having cubic forms as solutions52385244http://dx.doi.org/10.22436/jnsa.009.08.09ENWon-GilParkDepartment of Mathematics Education, College of Education, Mokwon University, Daejeon 35349, Republic of Korea.Jae-HyeongBaeHumanitas College, Kyung Hee University, Yongin 17104, Republic of Korea.In this paper, we obtain some results on the m-variable cubic functional equation
\[f(2x_1 + y_1,..., 2x_m + y_m) + f(2x_1 - y_1,..., 2x_m - y_m)\\
= 2f(x_1 + y_1,..., x_m + y_m) + 2f(x_1 - y_1,..., x_m - y_m) + 12f(x_1,..., x_m).\]
The cubic form \(f(x_1,..., x_m) =
\sum_{1\leq i\leq j\leq k\leq m} a_{ijk}x_ix_jx_k\) is a solution of the above functional equation.http://www.isr-publications.com/jnsa/2596/download-a-multi-dimensional-functional-equation-having-cubic-forms-as-solutionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830On the fixed point theory in bicomplete quasi-metric spaces52455251http://dx.doi.org/10.22436/jnsa.009.08.10ENCarmenAlegreInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.HacerDağDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.SalvadorRomagueraInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.PedroTiradoInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.We show that some important fixed point theorems on complete metric spaces as Browder's fixed point
theorem and Matkowski's fixed point theorem can be easily generalized to the framework of bicomplete
quasi-metric spaces. From these generalizations we deduce quasi-metric versions of well-known fixed point
theorems due to Krasnoselskiĭ and Stetsenko; Khan, Swalesh and Sessa; and Dutta and Choudhury, respectively. In fact, our approach shows that many fixed point theorems for \(\varphi\)-contractions on bicomplete
quasi-metric spaces, and hence on complete G-metric spaces, are actually consequences of the corresponding
fixed point theorems for complete metric spaces.
http://www.isr-publications.com/jnsa/2778/download-on-the-fixed-point-theory-in-bicomplete-quasi-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830Strong convergence theorem for common solutions to quasi variational inclusion and fixed point problems52525258http://dx.doi.org/10.22436/jnsa.009.08.11ENXianzhiTangDepartment of of basic courses, Yellow River Conservancy Technical Institute, Kaifeng 475004, China.HuanhuanCuiDepartment of Mathematics, Luoyang Normal University, Luoyang, 471022, China.In this paper, we consider a problem that consists of finding a common solution to quasi variational
inclusion and fixed point problems. We first present a simple proof to the strong convergence theorem
established by Zhang et al. recently. Next, we propose a new algorithm to solve such a problem. Under
some mild conditions, we establish the strong convergence of iterative sequence of the proposed algorithm.
http://www.isr-publications.com/jnsa/2836/download-strong-convergence-theorem-for-common-solutions-to-quasi-variational-inclusion-and-fixed-point-problemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830Multivalent guiding functions in the bifurcation problem of differential inclusions52595270http://dx.doi.org/10.22436/jnsa.009.08.12ENSergeyKornevFaculty of Physics and Mathematics, Voronezh State Pedagogical University, Lenina 86, 394043 Voronezh, Russia.Yeong-ChengLiouDepartment of Healthcare Administration and Medical Informatics; and Research Center of Nonlinear Analysis and Optimization and Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan.In this paper we use the multivalent guiding functions method to study the bifurcation problem for differential inclusions with convex-valued right-hand part satisfying the upper Carathéodory and the sublinear
growth conditions.
http://www.isr-publications.com/jnsa/2733/download-multivalent-guiding-functions-in-the-bifurcation-problem-of-differential-inclusionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830On the Meir-Keeler-Khan set contractions52715280http://dx.doi.org/10.22436/jnsa.009.08.13ENChi-MingChenDepartment of Applied Mathematics, National Hsinchu University of Education, Taiwan.ErdalKarapınarAtılım University Department of Mathematics 06586 Incek, Ankara, Turkey.Guang-TingChenDepartment of Applied Mathematics, National Hsinchu University of Education, Taiwan.This report is aim to investigate the fixed points of two classes of Meir-Keeler-Khan set contractions
with respect to the measure of noncompactness. The proved results extend a number of recently announced
theorems on the topic.
http://www.isr-publications.com/jnsa/1995/download-on-the-meir-keeler-khan-set-contractionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830Quenching for a parabolic system with general singular terms52815290http://dx.doi.org/10.22436/jnsa.009.08.14ENHaijiePeiCollege of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China.ZhongpingLiCollege of Mathematics and Information, China West Normal University, Nanchong 637009, P. R. China.In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary
conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are
obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some
appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is
non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in
this article.http://www.isr-publications.com/jnsa/2843/download-quenching-for-a-parabolic-system-with-general-singular-termsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830Further result on \(\mathcal{H}_\infty\) state estimation of static neural networks with interval time-varying delay52915305http://dx.doi.org/10.22436/jnsa.009.08.15ENXiaojunZhangSchool of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.XinWangSchool of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.ShoumingZhongSchool of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.This paper considers the \(\mathcal{H}_\infty\) state estimation problem of static neural networks with interval timevarying
delay. By constructing a suitable Lyapunov-Krasovskii functional, the single-integral and doubleintegral
terms in the time derivative of the Lyapunov functional are handled by utilizing the inverses of
first-order and squared reciprocally convex parameters techniques. An improved delay dependent criterion
is established such that the error system is globally asymptotically stable with \(\mathcal{H}_\infty\) performance. The desired
estimator gain matrix and the optimal performance index are obtained via solving a convex optimization
problem subject to linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness
of the proposed method.
http://www.isr-publications.com/jnsa/2844/download-further-result-on-mathcalh-infty-state-estimation-of-static-neural-networks-with-interval-time-varying-delayInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19019820160830Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications53065315http://dx.doi.org/10.22436/jnsa.009.08.16ENXiaoyanZhangSchool of Mathematics, Shandong University, Jinan 250100, Shandong, China.This paper is concerned with a class of mixed non-monotone tripled operators under the general conditions
of ordering relations in ordered Banach spaces. By means of the cone theory and technique of
equivalent norms, the existence and uniqueness of fixed points for such tripled operators are established.
The proof method in this paper is different from those used in the former relevant theorems. At last, an
application is presented to illustrate our result. We extend some previous existing results.
http://www.isr-publications.com/jnsa/2593/download-fixed-points-of-mixed-non-monotone-tripled-operators-in-ordered-banach-spaces-and-applications