AIMS Mathematics (May 2024)

Common fixed points for ($ \kappa _{G_{m}} $)-contractions with applications

  • Jamshaid Ahmad ,
  • Abdullah Shoaib,
  • Irshad Ayoob,
  • Nabil Mlaiki

DOI
https://doi.org/10.3934/math.2024772
Journal volume & issue
Vol. 9, no. 6
pp. 15949 – 15965

Abstract

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In this publication, our objective was to introduce and establish the concepts of $ \kappa _{G_{m}} $-contraction and generalized $ (\alpha, \kappa _{G_{m}}) $-contraction in complete $ G_{m} $-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis.

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