Coupled coincidence point theorems for mixed monotone nonlinear operators

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Abstract

We obtain coupled coincidence and coupled common fixed point theorems for mixed g-monotone nonlinear operators F:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and irić [V. Lakshmikantham, L. irić, 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. © 2012 Elsevier Ltd. All rights reserved.

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Berinde, V. (2012). Coupled coincidence point theorems for mixed monotone nonlinear operators. Computers and Mathematics with Applications, 64(6), 1770–1777. https://doi.org/10.1016/j.camwa.2012.02.012

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