Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Fixexd point theory and applications

Tsz-leung Yip¹  Xue-song Li² 

[1] Department of Logistics and Maritime Studies, Faculty of Business, Hong Kong Polytechnic University, Hong Kong, P.R. China;Department of Mathematics, Sichuan University, Chengdu, P.R. China

关键词: common fixed point;    △-convergence;    nonexpansive semigroup;    CAT(0) space;    implicit approximation;   

DOI  :  10.1186/1687-1812-2012-145

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the △-convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Mann iteration schemes with bounded perturbations for nonexpansive semigroups in CAT(0) spaces. The results presented in this paper extend and enrich the existing literature. MSC:47H05, 47H10, 47J25.

【 授权许可】

CC BY