Coupled coincidence point theorems for mixed monotone nonlinear operators

We obtain coupled coincidence and coupled common fixed point theorems for mixed gg-monotone nonlinear operators F:X×X→XF:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341–4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] and also include as particular cases several related results in very recent literature.