Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces

By Laurentiu Leustean. 2008

150 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/710c7f6b400117f9c434507e6ccd7595d98385b5

How researchers see this paper

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In Computational Theory and Mathematics

1. Genaro López-Acedo
2. David Ariza-Ruiz
3. Laurentiu Leustean
4. Ulrich Kohlenbach
5. Lavinia Corina Ciungu

In Control and Systems Engineering

1. Genaro López-Acedo
2. David Ariza-Ruiz
3. Laurentiu Leustean

In Geometry and Topology

1. Genaro López-Acedo
2. David Ariza-Ruiz
3. Laurentiu Leustean
4. Ulrich Kohlenbach

Citations in the corpus

• Firmly nonexpansive mappings in classes of geodesic spaces (2012, methodology): “Following [30], we shall refer to uniformly convex W -hyperbolic spaces with a monotone modulus of uniform convexity as UCW -hyperbolic spaces.”