Nonlinear ergodic theorems and weak convergence theorems for reversible semigroup of asymptotically nonexpansive mappings in Banach spaces

Fixexd point theory and applications

Lanping Zhu¹  Gang Li¹  Qianglian Huang¹ 

[1] College of Mathematics, Yangzhou University, Yangzhou, China

关键词: reversible semigroups;    Kadec-Klee property;    asymptotically nonexpansive mapping;    almost orbit;    uniformly convex Banach space;   

DOI  :  10.1186/1687-1812-2013-231

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we provide the nonlinear ergodic theorems and weak convergence theorems for almost orbits of a reversible semigroup of asymptotically nonexpansive mappings in a uniformly convex Banach space without assuming that X has a Fréchet differentiable norm. Since almost orbits in this paper are not almost asymptotically isometric, new methods have to be introduced and used for the proofs. Our main results include many well-known results as special cases and are new even for reversible semigroup of nonexpansive mappings. MSC:47H20.

【 授权许可】

CC BY