Fixed points for mappings of asymptotically nonexpansive type
Functional Analysis
2022-01-11 v1
Abstract
We prove the existence of a fixed point for mappings which satisfy some asymptotic nonexpansive conditions in Banach spaces which are either nearly uniformly convex or they satisfy that asymptotic centers of bounded sequences are compact. Nominally, we consider pointwise eventually nonexpansive mappings, pointwise asymptotically nonexpansive mappings and asymptotically type nonexpansive. We do not assume the existence of a continuous iterated, solving some long-standing open questions about existence of a fixed point for these mappings in absence of continuity.
Cite
@article{arxiv.2201.02802,
title = {Fixed points for mappings of asymptotically nonexpansive type},
author = {Tomas Dominguez Benavides and Pepa Lorenzo},
journal= {arXiv preprint arXiv:2201.02802},
year = {2022}
}