Common Fixed Point Results for Almost <i>ℛ_g</i>-Geraghty Type Contraction Mappings in <i>b</i>₂-Metric Spaces with an Application to Integral Equations

Abstract

In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of b2-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost g-α-η Geraghty type contraction mappings in b2-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered b2-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.

Keywords

• <i>b</i>₂-metric space
• fixed point
• binary relation
• almost <i>ℛ_g</i>-Geraghty type contraction