Coupled Optimal Results with an Application to Nonlinear Integral Equations

Abstract

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

“…The idea of coupled fixed points was generalized for coupled best-proximity points [10]. There are applications of coupled fixed points in different fields of mathematics-impulsive differential equations [6], integral equations [11], ordinary differential equations [12], periodic boundary value problems [13], fractional equations [14], and nonlinear matrix equations [15]-and in other scienceseconomics [16,17], aquatic ecosystems [18], and dynamic programming [19]-with these just being the most recent investigations dealing with coupled fixed points.…”