Fixed point results in generalized Branciari b-metric spaces with applications

Abstract

In 2000, A. Branciari introduced rectangular metric space replacing the triangular inequality
with more general inequality, namely, rectangular inequality (involving four points instead of three) in metric
space. The rectangular inequality was generalized by adding two more terms to the right hand of rectangular
inequality to introduce generalized Branciari metric space by A. Kostic [2] in 2025. In this paper, we extend
this further by multiplying it with a variable in order to introduce the generalized Branciari b-metric space.
We establish fixed point results for Banach contractions and Kannan contractive mappings in order to improve
existing literature. The validity of the result is evidenced by an example. We construct an example in support
of our theorem. Furthermore, we establish the existence and uniqueness of the Fredholm integral equation.