Copyright © 2009 Wei Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.