Berinde-type generalized $$$\alpha-\beta-\psi$$$ contraction in extended $$$S_{b}$$$-metric spaces

S. Fahed; M. Asif

doi:10.15421/242431

Berinde-type generalized $$$\alpha-\beta-\psi$$$ contraction in extended $$$S_{b}$$$-metric spaces

S. Fahed (Gomal University Dera Ismail Khan), https://orcid.org/0009-0003-0134-6927
M. Asif (University of Management and Technology, Sialkot), https://orcid.org/0000-0001-5684-4737

Abstract

In this paper, we extend the idea of Berinde-Type generalized $$$\alpha-\beta-\psi$$$ contractive mappings in the setting of complete extended $$$S_{b}$$$-metric spaces providing a significant advancement in fixed-point theory. The findings extend fixed point theory beyond metric spaces to $$$S_{b}$$$-metric spaces, offering a broader range of applications in optimization, nonlinear analysis and mathematical modelling. Non-trivial examples of the findings are provided to validate our claims. These examples demonstrate the potential of the proposed mappings for solving real-world phenomena. The work also suggests intriguing future research directions, such as generalizing fixed-point theorems and applying them to disciplines like dynamical systems and integral equations.

Keywords

analysis; extended $$$S_{b}$$$-metric spaces; fixed point theorem; Berinde-Type generalized $$$\alpha-\beta-\psi$$$ contraction

MSC 2020

Pri 47H09, Sec 47H10, 54H25

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