Fixed point results in complex valued extended $b$-metric spaces and related applications

Abstract

In this paper, some fixed point results of single-valued mappings satisfying a rational contraction in complex valued extended $b$-metric spaces are established. Nontrivial examples which support the hypotheses of the established idea herein are provided. Moreover, sufficient conditions for existence of a unique solution of nonlinear integral equation is considered to show a usability of the established concepts. Our result, being discussed in the setting of extended $b$-metric spaces improves a few fixed point theorems in the framework of complex valued metric and $b$-metric spaces in the comparable literature.