Ball Proximinal Spaces

The notion of ball proximinality and the strong ball proximinality were recently introduced by P. Bandyopadhyay, Bor-Luh Lin and T. S. S. R. K. Rao ["Ball proximinality in Banach spaces", Banach spaces and their Applications in Analysis, Proceedings of the Conference in Honor of Nigel Kalton's 60-th Birthday, B. Randrianantoanina et al. (eds.), Berlin: Walter de Gruyter, (2007) 251--264]. We prove that spaces with strong 3/2-ball property are ball proximinal and in particular M-ideals are ball proximinal. We show that the problem of ball proximinality of hyperplanes is related to the problem of proximinality of certain convex sets determined by them.