Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces
Functional Analysis
2008-10-23 v1 Logic
Abstract
We propose the class of uniformly convex -hyperbolic spaces with monotone modulus of uniform convexity (-hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. -hyperbolic spaces are a natural generalization both of uniformly convex normed spaces and CAT(0)-spaces. Furthermore, we apply proof mining techniques to get effective rates of asymptotic regularity for Ishikawa iterations of nonexpansive self-mappings of closed convex subsets in -hyperbolic spaces. These effective results are new even for uniformly convex Banach spaces.
Cite
@article{arxiv.0810.4117,
title = {Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces},
author = {Laurentiu Leustean},
journal= {arXiv preprint arXiv:0810.4117},
year = {2008}
}