Existence of fixed point in intuitionistic fuzzy b-metric space with application

Abstract

In this paper, extended intuitionistic fuzzy b-metric space is defined and showing the properties crucial to its structure. Subsequently, the fixed point theorem within the framework of these extended intuitionistic fuzzy b-metric spaces has been established. Our findings not only extend but also generalize the existing results in the current literature, demonstrating symmetrical patterns and properties within these mathematical frameworks. To underscore the effectiveness of the proposed methodologies, a nontrivial example is employed. Additionally, application related to the existence and uniqueness of solutions for a specific class of Fredholm integral equations is explored to highlight the practical implications of our main results.