Fixed point theorems for generalized $(\alpha ,\psi )$-contraction mappings in rectangular quasi b-metric spaces

Abstract

In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized $(\alpha ,\psi ) $ ( α , ψ ) -contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results in the literature, in particular, the works of Karapinar and Lakzian (J. Funct. Spaces 2014:914398, 2014), Alharbi et al. (J. Math. Anal. 9(3):47–60, 2018), and Khuangsatung et al. (Thai J. Math. 2020:89–101, 2020) from rectangular quasi metric space and rectangular b-metric space to rectangular quasi b-metric spaces. We also provide examples in support of our main findings. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.

Some New Types of α_(β^(-1) )-admissible Mappings and Fixed Point Results

“…Almost researchers in this direction have used 𝛼-admissible condition. For example see [8], [9], [10], [11], [12], [13], [14], [15].…”