The Mann algorithm in a complete geodesic space with curvature bounded above

Fixexd point theory and applications

Pongsakorn Yotkaew¹  Yasunori Kimura²  Satit Saejung³ 

[1] Centre of Excellence in Mathematics, CHE, Bangkok, Thailand;Department of Information Science, Toho University, Miyama, Japan;Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand

关键词: fixed point;    Mann algorithm;    nonexpansive mapping;    quasi-nonexpansive mapping;    Δ-convergence;   

DOI  :  10.1186/1687-1812-2013-336

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to prove two Δ-convergence theorems of the Mann algorithm to a common fixed point for a countable family of mappings in the case of a complete geodesic space with curvature bounded above by a positive number. The first one for nonexpansive mappings improves the recent result of He et al. (Nonlinear Anal. 75:445-452, 2012). The last one is proved for quasi-nonexpansive mappings and applied to the problem of finding a common fixed point of a countable family of quasi-nonexpansive mappings. MSC:49J53.

【 授权许可】

CC BY