Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-contractions in Uniformly Smooth Banach Spaces  

作　　者：Gang CAI 

机构地区：[1]College of Mathematics Science, Chongqing Normal University

出　　处：《Acta Mathematica Sinica,English Series》2015年第9期1435-1448,共14页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11171172 and 11401063);the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120002110044);the Natural Science Foundation of Chongqing(Grant No.cstc2014jcyj A00016)

摘　　要：The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.

关 键 词：Variational inequality fixed point strong convergence uniformly smooth Banach space 

分 类 号：O177.2[理学—数学]