English

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 FF has the following properties: there is a unique sequence of successive approximations and this sequence converges to a fixed point of FF. 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.

Keywords

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

R2 v1 2026-06-24T10:04:44.515Z