Fixed Point Results for -Rational Contraction in Complete Metric Spaces

  • Authors

    • Anas Yusuf Department of Mathematics, Federal University, Birnin Kebbi, Kebbi State, Nigeria
    • Almustapha Umar Department of Mathematics, Federal University, Birnin Kebbi, Kebbi State, Nigeria
    https://doi.org/10.14419/hgz0m151

    Received date: December 2, 2025

    Accepted date: January 8, 2026

    Published date: February 1, 2026

  • Complete metric space; Fixed point theorem; Nonlinear contractive mapping; Picard iteration; \theta-rational contraction

  • Abstract

    This paper introduces and investigates a new family of nonlinear contraction-type mappings, termed -rational contractions, defined on complete metric spaces. This class is formulated through a function  satisfying appropriate monotonicity and asymptotic regularity conditions, and incorporates both rational-type expressions and power-type nonlinearities. The proposed framework unifies and extends several well-known contractive conditions, including the Jleli-Samet -contractions and the rational-type contractions of Dass-Gupta. A general fixed point theorem is established, ensuring that a fixed point exist and is unique  for -rational contractions, together with the convergence of the associated Picard iteration. A corollary shows that, by choosing , the contractive condition reduces to a strict -contraction, thereby generalizing and strengthening the -contraction introduced by Jleli and Samet. Illustrative examples on both finite and continuous metric spaces are included to show the applicability of the established findings. Additionally, a common fixed point result is established for commuting pairs of -rational contractions. These results highlight the flexibility of the -rational framework and offer a unified approach to a broad class of nonlinear contractive conditions.

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  • How to Cite

    Yusuf, A., & Umar, A. (2026). Fixed Point Results for -Rational Contraction in Complete Metric Spaces. Global Journal of Mathematical Analysis, 12(1), 1-6. https://doi.org/10.14419/hgz0m151