R-weak commutativity, examples, and applications

Kütükcü S.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.37, no.1, pp.925-941, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1002/num.22576
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.925-941
  • Keywords: combined common fixed point, damped harmonic oscillator, integral type equation, non&#8208, Archimedean Menger probabilistic metric space, nonlinear matrix equation, R&#8208, weak commuting maps, Volterra type integral equation, FIXED-POINT THEOREMS, COMMUTING MAPPINGS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The aim of this article is to define a new contraction and its variants in non-Archimedean Menger probabilistic metric-spaces, and utilize them to establish the existence of a combined common fixed point illustrating with examples. We also apply our result to integral type equations, Volterra type integral equations, damped harmonic oscillators, and nonlinear matrix equations.