Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 108343, 11 pages
doi:10.1155/2010/108343
Fixed point theorems for nonlinear operators with and without monotonicity in partially ordered Banach spaces
Hui-Sheng Ding1
, Jin Liang2
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
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.