Coupled fixed point theorems for nonlinear contractions without mixed monotone property
1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand
2 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Korea
Fixed Point Theory and Applications 2012, 2012:170 doi:10.1186/1687-1812-2012-170Published: 3 October 2012
In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented.
MSC: 47H10, 54H25.