Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems  

作　　者：Shi Sheng ZHANG Chi Kin CHAN H.W.JOSEPH LEE 

机构地区：[1]College of Statistics and Mathematics,Yunnan Uniersity of Finance and Economics [2]Department of Applied Mathematics,The Hong Kong Polytechnic University

出　　处：《Acta Mathematica Sinica,English Series》2012年第4期741-758,共18页数学学报（英文版）

基　　金：Supported by Natural Science Foundation of Yibin University(Z-2009,No.3)

摘　　要：The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

关 键 词：Modified block iterative algorithm quasi-φ-asymptotically nonexpansive mapping quasi-φ-nonexpansive mapping relatively nonexpansive mapping generalized projection 

分 类 号：O177[理学—数学]