A hybrid fixed point theorem for product of two operators in a lattice-ordered Banach algebra with applications to quadratic integral equations

Abstract

We prove a hybrid fixed point theorem for the product of two operators in a latticeordered Banach algebra and apply to nonlinear hybrid quadratic integral equations of mixed type for proving the existence of maximal and minimal positive integrable solutions under certain mixed conditions of Lipschitzicity and monotonicity of the nonlinear functions. Our main existence result is illustrated with a numerical example as well as with an application to IVPs of nonlinear first-order discontinuous quadratically perturbed ordinary differential equations.