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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]

Abstract: We introduce some notions of generalized nonlinear contractive maps and prove some fixed point results for such maps. Consequently, several known fixed point results are either improved or generalized including the corresponding recent fixed point results of Ciric [L.B. Ciric, Multivalued nonlinear contraction mappings, Nonlinear Anal. 71 (2009) 2716–2723], Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132–139], Feng and Liu [Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103–112] and Mizoguchi and Takahashi [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177–188]. [Copyright &y& Elsevier]