Coupled Coincidence and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces

Wutiphol Sintunavarat, Poom Kumam

Abstract

The purpose of this paper is to prove some coupled coincidence point theorems for nonlinear contraction mappings having a mixed monotone property in a partially ordered metric spaces. We also give some examples to validate the main results in this paper. Our theorems are generalizations of the results of Luong and Thuan in [N.V. Luong, N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983–992.], classical coupled fixed point theorems of Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393.] and several results in fixed point theory.