Coupled fixed point theorems in partially ordered metric spaces and application

In this paper, we prove some coupled fixed point theorems for contractive mappings in partially ordered complete metric spaces under certain conditions to extend and complement the recent fixed point theorems according 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] and Luong and Thuan [N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74(2011), 983–992]. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations. AMS subject classifications: Primary 47H10; Secondary 54H25

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