Subinvariant metric functionals for nonexpansive mappings
Functional Analysis
2025-07-17 v1 Optimization and Control
Abstract
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed points of nonexpansive mappings. To demonstrate this, we additionally investigate subsets of Banach spaces that have only nontrivial metric functionals. We particularly show that in certain cases every metric functional has a unique minimizer; thus, subinvariance implies the existence of a fixed point.
Cite
@article{arxiv.2407.04234,
title = {Subinvariant metric functionals for nonexpansive mappings},
author = {Armando W. Gutiérrez and Olavi Nevanlinna},
journal= {arXiv preprint arXiv:2407.04234},
year = {2025}
}