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The existence and uniqueness of coupled best proximity point for proximally coupled contraction in a complete ordered metric space. (English) Zbl 1429.54056

Summary: We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379–1393 (2006; Zbl 1106.47047)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Citations:

Zbl 1106.47047
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References:

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