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Zbl 1206.54047
Karpagam, S.; Agrawal, Sushama
Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 4, 1040-1046 (2011). ISSN 0362-546X

Summary: We introduce a notion of cyclic orbital Meir-Keeler contraction and give sufficient conditions for the existence of fixed points and best proximity points of such a map. Our main result is a generalization of a best proximity point result due to {\it C. Di Bari, T. Suzuki} and {\it C. Vetro} [Nonlinear Anal., Theory Methods Appl. 69, No.~11, A, 3790--3794 (2008; Zbl 1169.54021)].

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: best proximity point; cyclic map; Meir-Keeler contraction

Citations: Zbl 1169.54021

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