Approximating solution for generalized quadratic functional integral equations with maxima

Abstract

In this paper we prove an existence as well as approximation result for a certain nonlinear generalized quadratic functional integral equation with maxima. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting with a lower or an upper solution converges monotonically to the solution of the related quadratic functional integral equation with maxima under some suitable mixed hybrid conditions. We base our main results on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space.An example illustrating the existence result is also presented.