Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive mappings in q -uniformly smooth Banach spaces

Fixexd point theory and applications

Zhiwei Xie¹  Ying Zhang² 

[1] School of Economics, Renmin University of China, Beijing, P.R. China;School of Mathematics and Physics, North China Electric Power University, Baoding, P.R. China

关键词: asymptotically strictly pseudocontractive mappings;    weak and strong convergence;    explicit averaging cyclic algorithm;    fixed points;    q-uniformly smooth Banach spaces;   

DOI  :  10.1186/1687-1812-2012-167

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong convergence of an explicit averaging cyclic process to a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings in q-uniformly smooth Banach spaces. The results of this paper are interesting extensions of those known results. MSC:47H09, 47H10.

【 授权许可】

CC BY