Fixed Point Results for Hybrid Rational Contractions under a New Compatible Condition with an Application

Abstract

In this scholarly discourse, we present proof of the existence of unique fixed points in b-metric spaces for hybrid rational contractions. Moreover, we establish a common fixed point theorem for four self-mappings, assuming S-compatibility for two pairs of self-mappings within the framework of b-metric spaces. As a practical demonstration of the aforementioned results, we apply them to a type of integral equation and derive a theorem that guarantees the existence of solutions.

Keywords

• fixed/common fixed point
• rational contraction
• <i>b</i>-metric space
• <i>C</i>-class function
• <i>S</i>-compatibility