Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces

Details Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces

2008-10-22

arxiv.org/abs/0810.4117v1

Mathematics

Functional Analysis

Scientific paper

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.

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