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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 191675, 9 pages
http://dx.doi.org/10.1155/2012/191675
Research Article

Existence and Uniqueness Theorems of Ordered Contractive Map in Banach Lattices

Center for Economic Research, Harbin University of Commerce, Harbin 150028, China

Received 18 September 2012; Accepted 5 November 2012

Academic Editor: Yongfu Su

Copyright © 2012 Xingchang Li and Zhihao Wang. 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.

Abstract

This paper presents some existence and uniqueness theorems of the fixed point for ordered contractive mapping in Banach lattices. Moreover, we prove the existence of a unique solution for first-order ordinary differential equations with initial value conditions by using the theoretical results with no need for using the condition of a lower solution or an upper solution.