Fixed Point Theorem for $\psi$-Geraghty Contraction Type Mappings in b-Metric Spaces with Application

Abstract

In this paper, we introduce a new class of contractive mappings, called generalized $\psi$-Geraghty contractions, in the framework of b-complete metric spaces. We establish a unique fixed-point theorem that extends existing results in fixed-point theory. An illustrative example with a graphical representation demonstrates the validity of our findings. Furthermore, we apply the main result to an integral equation, highlighting its effectiveness in ensuring the existence and uniqueness of solutions. This work underscores the theoretical significance and practical applicability of generalized $\psi$-Geraghty contractions in mathematics, physics, and engineering.

Key words: Fixed point, $\psi$-Geraghty contraction, b-metric space, nonlinear integral equations, existence and uniqueness.

Full Text

Article Information

Title	Fixed Point Theorem for $\psi$-Geraghty Contraction Type Mappings in b-Metric Spaces with Application
Source	Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 238-246
DOI	10.31392/MFAT-npu26_3.2025.07
Milestones	Received 22/08/2025; Revised 16/09/2025
Copyright	The Author(s) 2025 (CC BY-SA)

Authors Information

Sabita Kumari
Department of Mathematics, Shri Shankaracharya Professional University, Bhilai, 491001 Chhattisgarh, India

Sandip Shrivastava
Department of Mathematics, Shri Shankaracharya Professional University, Bhilai, 491001 Chhattisgarh, India

Shraddha Rajput
Department of Mathematics, Shri Shankaracharya Professional University, Bhilai, 491001 Chhattisgarh, India

Citation Example

Sabita Kumari, Sandip Shrivastava, and Shraddha Rajput, Fixed Point Theorem for $\psi$-Geraghty Contraction Type Mappings in b-Metric Spaces with Application, Methods Funct. Anal. Topology 31 (2025), no. 3, 238-246.

BibTex

@article {MFAT2127,
    AUTHOR = {Sabita Kumari and Sandip Shrivastava and Shraddha Rajput},
     TITLE = {Fixed Point Theorem for $\psi$-Geraghty Contraction Type Mappings in b-Metric Spaces with Application},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {31},
      YEAR = {2025},
    NUMBER = {3},
     PAGES = {238-246},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2025.07},
       URL = {https://mfat.imath.kiev.ua/article/?id=2127},
}

References

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