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Subinvariant metric functionals for nonexpansive mappings

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arxiv 2407.04234 v1 pith:2P6ZBEZD submitted 2024-07-05 math.FA math.OC

Armando W. Gutiérrez , Olavi Nevanlinna This is my paper · ORCID
classification math.FAmath.OC
keywords metricfunctionalsmappingsnonexpansivebanachexistencefixedinvestigate
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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.

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  1. Metric functionals and weak convergence

    math.FA 2025-06 accept novelty 6.0 of 10

    Convergence against all metric functionals equals classical weak convergence for bounded sequences in normed spaces.

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