Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces

Details Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces

2011-03-28

arxiv.org/abs/1103.5288v1

Mathematics

Functional Analysis

Scientific paper

We obtain coupled coincidence and coupled common fixed point theorems for mixed $g$-monotone nonlinear operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and \' Ciri\' c [Lakshmikantham, V., \' Ciri\' c, L., \textit{Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces}, Nonlinear Anal. \textbf{70} (2009), 4341-4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and also include as particular cases several related results in very recent literature.

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