Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

Shahnaz Jafari, Maryam Shams, Asier Ibeas, Manuel De La Sen

Research output: Contribution to journalArticleResearch

Abstract

© 2019, Lithuanian Association of Nonlinear Analysts. All rights reserved. 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.
Original languageEnglish
Pages (from-to)819-837
JournalNonlinear Analysis: Modelling and Control
Volume24
Issue number5
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Convergent sequence
  • Dynamic systems
  • Enhanced probabilistic metric space
  • Fixed point
  • Linear combination

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