Advances in Rational Contractions within Extended $b-$Metric Spaces and Their Applications

Authors

  • Haitham Ali Qawaqneh Department of Mathematics, Faculty of Science and Information Technology,, AlZaytoonah University of Jordan, Amman 11733, Jordan https://orcid.org/0000-0002-5495-1763
  • Gawhara Al-Musannef Faculty of Business Studies, Arab Open University, Jeddah, Saudi Arabia
  • Habes Alsamir Finance and Banking Department, Business Administration College,, Dar Aluloom University, Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v1i2.6056

Keywords:

Rational Contractions, fixed point theorem, Extended b-Metric Spaces

Abstract

This study introduces a novel class of rational contractions within the framework of extended b-metric spaces, extending classical fixed point theory to more generalized and flexible settings. We establish new fixed point theorems using a control function approach, which broadens the scope of contractive mappings that can be studied under extended b-metric spaces. The methodology combines analytical techniques with integral operator theory, allowing us to investigate the existence and uniqueness of solutions to both Volterra and Urysohn integral equations. To validate the theoretical results, illustrative examples and numerical simulations are presented, demonstrating the effectiveness and real-world relevance of the proposed framework.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Haitham Ali Qawaqneh, Gawhara Al-Musannef, Habes Alsamir

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How to Cite

Advances in Rational Contractions within Extended $b-$Metric Spaces and Their Applications. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6056. https://doi.org/10.29020/nybg.ejpam.v1i2.6056