Fixed Point Theory in Extended Parametric Sb-Metric Spaces and Its Applications

Abstract

This article introduces the novel concept of an extended parametric 𝑆𝑏-metric space, which is a generalization of both 𝑆𝑏-metric spaces and parametric 𝑆𝑏-metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps. We then prove an improved version of the Banach contraction principle for symmetric extended parametric 𝑆𝑏-metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integral equations, demonstrating the practical implications of our work.