On Series-Like Iterative Equation with a General Boundary Restriction

Abstract

Abstract By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation . Moreover, we get that the solution depends continuously on . As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation with a general boundary restriction, where is a given Lipschitz function, and are compact convex subsets of with nonempty interior.