Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces

Details Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces

2011-03-28

arxiv.org/abs/1103.5285v1

Mathematics

Functional Analysis

Scientific paper

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. TMA \textbf{65} (2006) 1379-1393] by significantly weakening the involved contractive condition. Our technique of proof is essentially different and more natural. An example as well an application to periodic BVP are also given in order to illustrate the effectiveness of our generalizations.

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