Existence of solution of functional Volterra-Fredholm integral equations in space L∞(ℝ+) and sinc interpolation to find solution

Abstract

A new measure of noncompactness (Mnc) and Darbo fixed point theorem are utilized on the space $L^{\infty }({ℝ}_{+})$ to prove the existence of solution for functional Volterra–Fredholm integral equations. An example is given to confirm the validity of results. Furthermore, we propound an iterative algorithm by sinc interpolation to find the solution with an acceptable accuracy. In this algorithm, it is not necessary for the problem to be discretized to an algebraic system with unknown coefficients. We also use an iterative process to approximate a solution with exponential convergence.