Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Generalized 𝜓-Geraghty-Zamfirescu Contraction Pairs in b-metric Spaces

  • Morales, Jose R. (Departamento de Matematicas, Universidad de Los Andes) ;
  • Rojas, Edixon M. (Departamento de Matematicas, Universidad Nacional de Colombia)
  • Received : 2020.09.13
  • Accepted : 2021.01.19
  • Published : 2021.06.30
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Abstract

The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points.

Keywords

Acknowledgement

The authors are thankful to the referee for the very constructive comments and suggestions that led to an improvement of the paper, particularly, in regards to the consideration of the Jungck-Ishikawa iteration.

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