Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one

Fixexd point theory and applications

Yasunori Kimura¹  Kenzi Satô² 

[1] Department of Information Science, Toho University, Miyama, Funabashi, Japan;Laboratory of Mathematics, Faculty of Engineering, Tamagawa University, Machida, Tokyo, Japan

关键词: Halpern iteration;    strongly quasinonexpansive;    Δ-demiclosed;    fixed point;   

DOI  :  10.1186/1687-1812-2013-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we deal with the Halpern iterative scheme for a strongly quasinonexpansive mapping in the setting of a complete geodesic space with curvature bounded above by one. Our result can be applied to the image recovery problem. We also consider the approximation of a fixed point of a nonexpansive mapping and obtain convergence theorems, one of which is a supplement of the result by Pia̧tek with an additional sufficient condition. MSC:47H09.

【 授权许可】

CC BY