Strong convergence theorems by Halpern-Mann iterations for multi-valued relatively nonexpansive mappings in Banach spaces with applications
نویسندگان
چکیده
* Correspondence: changss@yahoo. cn College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China Full list of author information is available at the end of the article Abstract In this article, an iterative sequence for relatively nonexpansive multi-valued mapping by modifying Halpern and Mann’s iterations is introduced, and then some strong convergence theorems are proved. At the end of the article some applications are given also. AMS Subject Classification: 47H09; 47H10; 49J25.
منابع مشابه
Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).
متن کاملStrong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces
In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings. Then, we give applications of our main results in equilibrium problems.
متن کاملFixed Point of a Countable Family of Uniformly Totally Quasi- Ø -Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications
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 ...
متن کاملApproximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces
We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpa...
متن کاملConvergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.
متن کامل