Common Fixed Points of Asymptotically Regular Mappings in Convex Metric Spaces with Application

Authors

  • Abdul Rahim Khan Department of Mathematics and statistics, Institute of Southern Punjab, Multan, Pakistan
  • Godwin Ugwunnadi Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini
  • Maggie Aphane Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa
  • Faizan Yousaf Department of Mathematics and statistics, Institute of Southern Punjab, Multan, Pakistan
  • Amir Abbas Department of Mathematics and statistics, Institute of Southern Punjab, Multan, Pakistan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5826

Keywords:

Common fixed point;, Gornicki-type contraction mapping;, Convex Metric Space;, Uniformly Convex Hyperbolic Space;, Asymptotically Regular Mapping;, Nonlinear Integral Equations;

Abstract

In this paper, based upon G\'{o}rnicki's work on fixed points of a continuous asymptotically regular self-mapping on a metric space, we establish common fixed point results for similar self-mappings and their average mappings on a convex metric space by using various types of contractive conditions. The closedness and convexity of the set of fixed points  of a non- self- mapping is obtained here in the  context of a  uniformly convex hyperbolic  space. We also apply our findings to solve Volterra type integral equations, demonstrating practical use of our work in mathematical analysis and its related fields.

Author Biography

  • Maggie Aphane, Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa

    Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Abdul Rahim Khan, Godwin Ugwunnadi, Maggie Aphane, Faizan Yousaf, Amir Abbas

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How to Cite

Common Fixed Points of Asymptotically Regular Mappings in Convex Metric Spaces with Application. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5826. https://doi.org/10.29020/nybg.ejpam.v18i2.5826