Orbital Lipschitzian mappings and semigroup actions on metric spaces
DOI:
https://doi.org/10.12775/TMNA.2023.058Keywords
Fixed points, actions of semigroups, metric spaces, uniform Lipschitzian mappings, Lifschitz constant, uniform normal structure, orbit-nonexpansive mappings, orbit Lipschitzian actionsAbstract
In this paper we study some results on common fixed points of families of mappings on metric spaces by imposing orbit Lipschitzian conditions on them. These orbit Lipschitzian conditions are weaker than asking the mappings to be Lipschitzian in the traditional way. We provide new results under the two classic approaches in the theory of fixed points for uniformly Lipschitzian mappings: the one under the normal structure property of the space (which can be regarded as the Cassini-Maluta's approach) and the one after the Lifschitz characteristic of the metric space (Lifschitz's approach). Although we focus on the case of semigroup of mappings, our results are new even when a mapping is considered by itself.References
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Copyright (c) 2024 Daniel Souza, Rafael Espínola, Maria Japón
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