The existence of best proximity points in metric spaces with the property UC
- Authors: Suzuki, T; Kikkawa, M; Vetro, C
- Publication year: 2009
- Type: Articolo in rivista (Articolo in rivista)
- Key words: Best proximity point; Property UC
- OA Link: http://hdl.handle.net/10447/40159
Abstract
Eldred and Veeramani in [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006. MR2260159] 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.