Existence and convergence of fixed points for mappings of asymptotically nonexpansive type in uniformly convex W-hyperbolic spaces

Fixexd point theory and applications

Jingxin Zhang¹  Yunan Cui² 

[1] Department of Mathematics, Harbin Institute of Technology, Harbin, China;Department of Mathematics, Harbin University of Science and Technology, Harbin, China

关键词: Asymptotically nonexpansive type;    Fixed points Δ-convergence;    Uniformly convex W-hyperbolic spaces;    CAT(0) spaces;   

DOI  :  10.1186/1687-1812-2011-39

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0) spaces. In this article, we discuss the existence of fixed points and demiclosed principle for mappings of asymptotically non-expansive type in uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity. We also obtain a Δ-convergence theorem of Krasnoselski-Mann iteration for continuous mappings of asymptotically nonexpansive type in CAT(0) spaces. MSC: 47H09; 47H10; 54E40.

【 授权许可】

CC BY