Rational contractions of the Geraghty and Dass-Gupta type in super metric spaces with applications

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Shah K., Khayyam Shah S., Sarwar M., Hleili M., Abdeljawad T.

Journal of Inequalities and Applications, vol.2025, no.1, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2025 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1186/s13660-025-03364-w
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: Boundary Value Problems, Chemical Reactor and Electric Circuits, F-contraction, Geraghty Contraction, Integral inclusion, Super Metric Space
  • Middle East Technical University Affiliated: Yes

Abstract

The purpose of this paper is to prove the fixed point results for rational contractions of the Geraghty and Dass-Gupta type in a super metric spaces. Unlike the other authors, we have only used the first two characteristics of Wardowski’s auxiliary functions F. Moreover, Geraghty-type contraction has been reconsidered to demonstrate its significance in a super metric spaces. In order to prove that the results are genuine, we give a few examples. Furthermore, the developed results are then utilized to demonstrate the behavior of exothermic chemical reactors and electrical circuit models and demonstrate the stability of the integral inclusions and Boundary value problems. We find this study intriguing because many problems can be solved using the super metric space, even when the usual metric doesn’t work.