
Journal of Convex Analysis 18 (2011), No. 2, 353366 Copyright Heldermann Verlag 2011 Ball Proximinal Spaces V. Indumathi Dept. of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014, India pdyindumath@gmail.com S. Lalithambigai Dept. of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014, India s_lalithambigai@yahoo.co.in The notion of ball proximinality and the strong ball proximinality were recently introduced by P. Bandyopadhyay, BorLuh 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 60th Birthday, B. Randrianantoanina et al. (eds.), Berlin: Walter de Gruyter, (2007) 251264]. We prove that spaces with strong 3/2ball property are ball proximinal and in particular Mideals 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. Keywords: Proximal, ball proximal, strongly ball proximal. [ Fulltextpdf (159 KB)] for subscribers only. 