Coupled and Tripled Coincidence Point Results with Application to Fredholm Integral Equations

Abstract

The aim of this paper is to define weak $\alpha$-$\psi$-$\phi$-contractive mappings and to establish coupled and tripled coincidence point theorems for such mappings defined on $G_b$-metric spaces using the concept of rectangular $G$-$\alpha$-admissibility. As an application, we derive new coupled and tripled coincidence point results for weak $\psi$-$\phi$-contractive mappings in partially ordered $G_b$-metric spaces. Our results are generalizations and extensions of some recent results in the literature. We also present an example as well as an application to nonlinear Fredholm integral equations in order to illustrate the effectiveness of our results.