The existence of best proximity points in metric spaces with the property UC. (English) Zbl 1178.54029

Authors’ abstract: A. A. Eldred and P. Veeramani [J. Math. Anal. Appl. 323, No. 2, 1001–1006 (2006; Zbl 1105.54021)] proved a theorem which ensures the existence of a best proximity point of cyclic contractions in the framework of uniformly convex Banach spaces. In this paper we introduce a notion of the property UC and extend the Eldred and Veeramani theorem to metric spaces with the property UC.


54H25 Fixed-point and coincidence theorems (topological aspects)


Zbl 1105.54021
Full Text: DOI


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