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.
Suzuki, T., Kikkawa, M., Vetro, C. (2009). The existence of best proximity points in metric spaces with the property UC. NONLINEAR ANALYSIS, 71(7-8), 2918-2926 [10.1016/j.na.2009.01.173].
The existence of best proximity points in metric spaces with the property UC
VETRO, Calogero
2009-01-01
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.
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