Open Access

On Series-Like Iterative Equation with a General Boundary Restriction

Fixed Point Theory and Applications20092009:892691

DOI: 10.1155/2009/892691

Received: 26 August 2008

Accepted: 4 February 2009

Published: 9 February 2009

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.

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Mathematics, Harbin Institute of Technology
(2)
Department of Applied Mathematics, Dalian University of Technology

Copyright

© Wei Song et al. 2009

This article is published under license to BioMed Central Ltd. 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.