A coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space with applications

Abstract

In this paper we prove a coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space and apply to a pair of nonlinear second order coupled linearly perturbed hybrid differential equations with the periodic boundary conditions for proving the existence and approximation of coupled solutions under certain mixed hybrid conditions. The abstract existence result of the coupled periodic boundary value problems is also illustrated by furnishing a numerical example.