On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples
De la Sen, Manuel (Universidad del País Vasco. Departamento de Electricidad y Electrónica)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)

Date:	2022
Abstract:	In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets (Formula presented. ) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed.
Grants:	Agencia Estatal de Investigación RTI2018-094336-B-I00
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Cyclic self-mappings ; Cyclic contractions ; Mixed cyclic/acyclic self-mappings ; Uniformly convex Banach space ; Impulsive dynamic systems ; Stabilization
Published in:	Mathematics, Vol. 10, Issue 14 (July 2022) , art. 2415, ISSN 2227-7390

DOI: 10.3390/math10142415

29 p, 2.5 MB

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