Year: 2008
Type: preprint
Abstract: We propose the class of uniformly convex $W$-hyperbolic spaces with monotone modulus of uniform convexity ($UCW$-hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. $UCW$-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 $UCW$-hyperbolic spaces. These effective results are new even for uniformly convex Banach spaces.
Source: arXiv (Cornell University)
Author: Leustean, Laurentiu
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1510478229