φ-fixed point results for nonlinear contractions with an application

Abstract

In this paper, using the notion of w-distance in metric spaces, we introduce two types of nonlinear contractions, (iota ,psi ,varphi ,phi ,p) and rational-(iota ,psi , varphi ,phi ,p) contractions. Based on these contractions, we prove the existence and uniqueness of a φ-fixed point for the corresponding contraction. We also provide some examples to demonstrate the correctness and practicability of our results, along with a numerical experiment. Finally, we apply the obtained results to linear matrix equations and nonlinear Fredholm integral equations.