Employing Weak $\psi -\varphi $ \ Contraction on Fuzzy Metric Spaces with Application

Abstract

We establish a common fixed point theorem satisfying a weak $\psi -\varphi $ contraction on partially ordered non-Archimedean fuzzy metric spaces. In the process, some multidimensional common fixed point results are derived from our main results. As an application, we study the existence of the solution to an integral equation and also give an example to show the usefulness of the obtained results. Our results generalize, extend and improve several well-known results of the existing literature.