Elegant Rational Contractive Conditions with Applications to Implicit Functional Integral Equations

Abstract

This paper aims to introduce several new classes of contraction mappings inspired by convex and rational contraction mappings. We establish the existence and uniqueness of fixed points for each newly proposed contraction mapping in metric spaces. To validate our theoretical findings, we provide several illustrative examples that demonstrate cases where well-known fixed point results, such as the Banach contraction principle, the Kannan fixed point theorem, the Chatterjea fixed point theorem, the Jaggi fixed point theorem, and the Istratescu fixed point theorem, are not applicable. As an application, we employ our theoretical fixed point results to investigate the existence and uniqueness of solutions to nonlinear implicit integral equations.