Intuitionistic Fuzzy Z-Contractions and Common Fixed Points with Applications

Authors

  • M. Rashid Department of Mathematics and Statistics,International Islamic University
  • Naeem Saleem Department of Mathematics University of Management and Technology, Lahore, Pakistan http://orcid.org/0000-0002-1485-6163
  • Q. Mumtaz Department of Mathematics and Statistics,International Islamic University;
  • Maggie Aphane Sefako Makgatho Health Sciences University
  • I. Rehman Dhofar University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5431

Keywords:

b-metric space, common intuitionistic fuzzy fixed point, intuitionistic fuzzy set-valued map, pairwise intuitionistic fuzzy Z-contraction, Simulation function

Abstract

In the context of $b$-metric spaces, this paper introduces two concepts: admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and pairwise admissible hybrid intuitionistic fuzzy $\mathcal{Z}$-contractions and establishes criteria for intuitionistic fuzzy fixed points under such contractions. It is demonstrated that a pair of set-valued maps possesses a common fixed point. Various illustrative examples are provided to validate these results. Moreover, the significant implications of our main theorem are explored and analyzed across different types of simulation functions. Furthermore, we derive several fixed point results in the context of partially ordered b-metric spaces, offering insights from an application-oriented perspective. These outcomes extend and generalize several prior results documented in the literature.

Author Biographies

  • M. Rashid, Department of Mathematics and Statistics,International Islamic University

    Associate Professor

  • Q. Mumtaz, Department of Mathematics and Statistics,International Islamic University;

    PhD Student

    Department of Mathematics and Statistics,International Islamic University;

  • Maggie Aphane, Sefako Makgatho Health Sciences University

    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Medunsa, Pretoria 0204, South Africa;

  • I. Rehman, Dhofar University

    Department of Mathematics and Sciences, College of Arts and Applied Sciences Dhofar University,
    Salalah, Oman

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 M. Rashid, Naeem Saleem, Q. Mumtaz, Maggie Aphane, I. Rehman

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How to Cite

Intuitionistic Fuzzy Z-Contractions and Common Fixed Points with Applications. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3304-3335. https://doi.org/10.29020/nybg.ejpam.v17i4.5431