Coupled Fixed Point Theorems for Contractive Mappings Involving New Function Classes and Applications

Abstract

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for contractive mappings involving new function classes in complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.