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A coupled coincidence point result in partially ordered metric spaces for compatible mappings. (English) Zbl 1229.54051
Summary: We introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result. Our work extends the work of T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)]. An example is also given.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E50 Complete metric spaces
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