Coupled Coincidence Points for Mixed Monotone Operators in Partially Ordered Metric Spaces

Abstract

In this paper, we give and prove some coupled coincidence point theorems for mappings F : X x X -> X and g : X -> X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65: 1379-1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4): 16-24, 2010), Harjani et al. (Nonlinear Anal 74: 1749-1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57: 1-16, 2011). We also give some examples to illustrate our results.