English

Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces

Functional Analysis 2008-10-23 v1 Logic

Abstract

We propose the class of uniformly convex WW-hyperbolic spaces with monotone modulus of uniform convexity (UCWUCW-hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. UCWUCW-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 UCWUCW-hyperbolic spaces. These effective results are new even for uniformly convex Banach spaces.

Keywords

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}
}
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