Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications

Fixexd point theory and applications

JC Yao¹  LC Ceng²  NC Wong³ 

[1] Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan;Department of Mathematics, Shanghai Normal University, Shanghai, China;Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China

关键词: hybrid viscosity approximation method;    nonexpansive mapping;    strictly convex Banach space;    uniformly smooth Banach space;    reflexive Banach space with weakly continuous duality map;   

DOI  :  10.1186/1687-1812-2012-117

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, let E be a reflexive and strictly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We consider the hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in E. We prove the strong convergence of this method to a common fixed point of the infinite family of nonexpansive mappings, which solves a variational inequality on their common fixed point set. We also give a weak convergence theorem for the hybrid viscosity approximation method involving an infinite family of nonexpansive mappings in a Hilbert space. MSC:47H17, 47H09, 47H10, 47H05.

【 授权许可】

CC BY