Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 108343, 11 pages
doi:10.1155/2010/108343
Research Article

Fixed Point Theorems for Nonlinear Operators with and without Monotonicity in Partially Ordered Banach Spaces

Hui-Sheng Ding,1 Jin Liang,2 and Ti-Jun Xiao3

1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
3Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 30 September 2009; Revised 5 December 2009; Accepted 6 December 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Hui-Sheng Ding 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.

Abstract

We establish two fixed point theorems for nonlinear operators on Banach spaces partially ordered by a cone. The first fixed point theorem is concerned with a class of mixed monotone operators. In the second fixed point theorem, the nonlinear operators are neither monotone nor mixed monotone. We also provide an illustrative example for our second result.