Approximating positive solutions of quadratic functional integral equations

Abstract

In this paper we prove the existence as well as approximations of the positive solutions for a nonlinear quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our results on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.