Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces
Jafari, Shahnaz (University of Shahrekord. Department of Pure Mathematics (Iran))
Shams, Maryam (University of Shahrekord. Department of Pure Mathematics (Iran))
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)
De la Sen, Manuel (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)

Date:	2019
Abstract:	In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples.
Grants:	Ministerio de Economía y Competitividad RT12018-094902-B-C22 Ministerio de Economía y Competitividad RT12018-094336-B-100
Note:	Altres ajuts: Basque Government for its support through grant IT1207-19
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:	Enhanced probabilistic metric space ; Fixed point ; Linear combination ; Convergent sequence ; Dynamic systems
Published in:	Nonlinear Analysis: Modelling and Control, Vol. 24, Issue 5 (2019) , p. 819-837, ISSN 2335-8963

DOI: 10.15388/NA.2019.5.8

19 p, 369.7 KB

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