Orbital Lipschitzian mappings and semigroup actions on metric spaces

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 t...

Descripción completa

Detalles Bibliográficos
Autores: Parasio Sobreira de Souza, Daniel, Espínola García, Rafael, Japón Pineda, María de los Ángeles
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/164767
Acceso en línea:https://hdl.handle.net/11441/164767
https://doi.org/10.12775/TMNA.2023.058
Access Level:acceso abierto
Palabra clave:Fixed points
Actions of semigroups
Metric spaces
Uniform Lipschitzian mappings
Lifschitz constant
Uniform normal structure
Orbit-nonexpansive mappings
Orbit Lipschitzian actions
Descripción
Sumario: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.