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 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.