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Best proximity points for cyclic Meir-Keeler contractions. (English) Zbl 1169.54021
Summary: We introduce a notion of cyclic Meir-Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir-Keeler contractions. This theorem is a generalization of a recent result due to A. A. Eldred and P. Veeramani [J. Math. Anal. Appl. 323, No. 2, 1001–1006 (2006; Zbl 1105.54021)].

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces