New Fixed Point Theorems for θ-ϕ-Contraction on Rectangular b -Metric Spaces

Abstract

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of $\theta -\varphi$-contraction in metric spaces, introduced by Zheng et al., we present the notion of $\theta -\varphi$-contraction in $b$-rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.