Convergence theorems of modified Mann iterations

Fixexd point theory and applications

Jinzuo Chen¹  Dingping Wu¹ 

[1] College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China

关键词: strong convergence;    modified Mann iteration;    uniformly convex Banach space;    asymptotically nonexpansive mapping;    nonexpansive semigroups;    asymptotically nonexpansive semigroups;    accretive operator;   

DOI  :  10.1186/1687-1812-2013-282

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce the modified iterations of Mann’s type for nonexpansive mapping and asymptotically nonexpansive mapping to have the strong and weak convergence in a uniformly convex Banach space. We also proved strong convergence theorems of our modified Mann’s iteration processes for nonexpansive semigroups and asymptotically nonexpansive semigroups. The results presented in the paper give a partially affirmative answer to the open question raised by Kim and Xu (Nonlinear Anal. 64:1140-1152, 2006). Applications to the accretive operators are also included. MSC:47H09, 47H10, 47J25.

【 授权许可】

CC BY