Coupled fixed point theorems for $\phi$-contractive mixed monotone mappings in partially ordered metric spaces

By Vasile Berinde. 2011

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In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0a0b092e26dc181c601e93c520651650fe32e420