SHAVETAMBRY TEJPAL and T. D. NARANG

On sets of unique best approximants

Pages 151-158
Received: 5 September 2006  
Mathematics Subject Classification (2000): 41A65, 41A50, 41A52

Abstract S. B. Steckin [Rev. Math. Pure Appl. 8 (1963), 5-18] proved that for a proximinal subset M of a strictly convex Banach space X, the set {x ∈ X : x has a unique best approximation in M} is dense in X and is a residual set in X if M is approximatively compact subset of X. We extend these results to convex metric spaces.