Firmly nonexpansive mappings in classes of geodesic spaces
Functional Analysis
2012-11-26 v3 Logic
Abstract
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, as (uniformly convex) -hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic egularity for the Picard iterations.
Cite
@article{arxiv.1203.1432,
title = {Firmly nonexpansive mappings in classes of geodesic spaces},
author = {David Ariza-Ruiz and Laurentiu Leustean and Genaro Lopez-Acedo},
journal= {arXiv preprint arXiv:1203.1432},
year = {2012}
}
Comments
typos corrected