A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

Abstract

In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed.

Keywords

• coupled common fixed point
• <i>F</i>-contraction mapping
• dynamic programming
• nonlinear integral equations