The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c...The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).展开更多
Some convergences of topology are discussed. The definitions of almost uniform convergence topology and compatible topology are given. It is shown that the quasiuniform convergence and generalized uniform convergence ...Some convergences of topology are discussed. The definitions of almost uniform convergence topology and compatible topology are given. It is shown that the quasiuniform convergence and generalized uniform convergence have no compatible topology,but the almost uniform convergence has compatible topology. Moreover, the description of all uniform convergence limits and their mutual relation are investigated[1].展开更多
In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki...In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki contraction in such spaces. Around our paper, the function <i>ψ</i> is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.展开更多
We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and sev...We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.展开更多
In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of to...In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.展开更多
In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric...In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.展开更多
Let I be a compact interval of real axis R, and （L, H） be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f ： I →L be a continuous multi-valued map. Assume that Pn = （x0,...Let I be a compact interval of real axis R, and （L, H） be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f ： I →L be a continuous multi-valued map. Assume that Pn = （x0, x1,..., xn） is a return trajectory of f and that p ∈ [min Pn, max Pn] with p ∈ f（p）. In this paper, we show that if there exist k （≥ 1） centripetal point pairs of f （relative to p） in {（xi;xi＋l） ： 0 ≤ i ≤ n- 1} and n =sk＋r （0 ≤ r ≤ k - 1）, then f has an R-periodic orbit, where R=s＋1 ifsiseven, and R =s if s is odd and r = 0, and R=s＋2 if s is odd and r 〉0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to L.展开更多
The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly mono...The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich（Ekonomika i Matematicheskie Metody,1976,12（4）：747-756）,but also extend and replenish the corresponding results obtained by Iiduka and Takahashi（Nonlinear Anal TMA,2005,61（3）：341-350）,Takahashi and Toyoda（J Optim Theory Appl,2003, 118（2）：417-428）,Nadezhkina and Takahashi（J Optim Theory Appl,2006,128（1）：191- 201）,and Zeng and Yao（Taiwan Residents Journal of Mathematics,2006,10（5）：1293-1303）.展开更多
With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is d...With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the （2＋1）-dimensional NNV system.展开更多
The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating ...The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.展开更多
In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. ...In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer＇s fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.展开更多
In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one...In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schacfer＇s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.展开更多
文摘The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).
文摘Some convergences of topology are discussed. The definitions of almost uniform convergence topology and compatible topology are given. It is shown that the quasiuniform convergence and generalized uniform convergence have no compatible topology,but the almost uniform convergence has compatible topology. Moreover, the description of all uniform convergence limits and their mutual relation are investigated[1].
文摘In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki contraction in such spaces. Around our paper, the function <i>ψ</i> is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.
基金supported by Grant No.174025 of the Ministry of Science,Technology and Development,Republic of Serbiasupported by Universita` degli Studi di Palermo,Local project R.S.ex 60%
文摘We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.
文摘In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.
文摘In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.
基金Supported by NNSF of China(Grant No.11761011)NSF of Guangxi(Grant Nos.2016GXNSFBA380235and 2016GXNSFAA380286)+1 种基金YMTBAPP of Guangxi Colleges(Grant No.2017KY0598)SF of Guangxi Univresity of Finance and Economics(Grant No.2017QNA04)
文摘Let I be a compact interval of real axis R, and （L, H） be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f ： I →L be a continuous multi-valued map. Assume that Pn = （x0, x1,..., xn） is a return trajectory of f and that p ∈ [min Pn, max Pn] with p ∈ f（p）. In this paper, we show that if there exist k （≥ 1） centripetal point pairs of f （relative to p） in {（xi;xi＋l） ： 0 ≤ i ≤ n- 1} and n =sk＋r （0 ≤ r ≤ k - 1）, then f has an R-periodic orbit, where R=s＋1 ifsiseven, and R =s if s is odd and r = 0, and R=s＋2 if s is odd and r 〉0. Besides, we also study stability of periodic orbits of continuous multi-valued maps from I to L.
基金the Natural Science Foundation of Yibin University of China(No.2007-Z003)
文摘The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich（Ekonomika i Matematicheskie Metody,1976,12（4）：747-756）,but also extend and replenish the corresponding results obtained by Iiduka and Takahashi（Nonlinear Anal TMA,2005,61（3）：341-350）,Takahashi and Toyoda（J Optim Theory Appl,2003, 118（2）：417-428）,Nadezhkina and Takahashi（J Optim Theory Appl,2006,128（1）：191- 201）,and Zeng and Yao（Taiwan Residents Journal of Mathematics,2006,10（5）：1293-1303）.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Scientific Research Foundation of Zhejiang Provincial Education Department under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001
文摘With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the （2＋1）-dimensional NNV system.
基金supported by the Natural Science Foundation of Yibin University (No.2009-Z003)
文摘The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.
文摘In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer＇s fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.
文摘In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schacfer＇s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.
