Viscosity approximation methods for asymptotically nonexpansive mapping in CAT(0) spaces

Fixexd point theory and applications

Uraiwan Boonkong¹  Rabian Wangkeeree²  Pakkapon Preechasilp² 

[1] Centre of Excellence in Mathematics, CHE, Bangkok, Thailand;Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand

关键词: viscosity approximation method;    asymptotically nonexpansive mapping;    variational inequality;    CAT(0) space;    common fixed point;   

DOI  :  10.1186/s13663-015-0273-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let C be a nonempty, closed, and convex subset of a complete CAT(0) space X and let T be an asymptotically nonexpansive mapping of C into itself such that the set of common fixed points of T is nonempty. We introduce the iterative schemes for finding the common fixed point of an asymptotically nonexpansive mapping which is the unique solution of some variational inequalities. The strong convergence theorem of the proposed iterative schemes is established. Our result improves and generalizes several other results in the literature.

【 授权许可】

CC BY