On Successive Approximations for Compact-Valued Nonexpansive Mappings
Functional Analysis
2023-08-14 v4
Abstract
We show that for a given initial point the typical, in the sense of Baire category, nonexpansive compact valued mapping has the following properties: there is a unique sequence of successive approximations and this sequence converges to a fixed point of . In the case of separable Banach spaces we show that for the typical mapping there is a residual set of initial points that have unique trajectory.
Cite
@article{arxiv.2203.03470,
title = {On Successive Approximations for Compact-Valued Nonexpansive Mappings},
author = {Emir Medjic},
journal= {arXiv preprint arXiv:2203.03470},
year = {2023}
}
Comments
Improved Sections 4 and 6, Version accepted for publication after peer review