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Abstract: In this paper, we extend the coupled fixed point theorems for mixed monotone operators obtained by 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 Luong and Thuan [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983–992], by weakening the involved contractive condition. An example as well as an application to nonlinear Fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the coupled fixed point theorems for mixed monotone operators obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] by significantly weakening the contractive condition involved. Our technique of proof is essentially different and more natural. An example as well as an application to periodic BVP is also given in order to illustrate the effectiveness of our generalizations. [Copyright &y& Elsevier]