Subinvariant Metric Functionals for Nonexpansive Mappings
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.
Type
Publication
Numerical Functional Analysis and Optimization, 46(8-9), 725–742
Status
Peer-reviewed
Open access
Main results
Authors
Research Scientist
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.