Abstract

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 1121\frac{1}{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.

Author information

Contact details are reproduced from the original publication and may be historical.

V. Indumathi

Dept. of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014, India

pdyindumath@gmail.com

Keywords

  • Proximinal
  • ball proximinal
  • strongly ball proximinal

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Suggested citation

V. Indumathi, S. Lalithambigai. “Ball Proximinal Spaces.” Journal of Convex Analysis 18 (2011), No. 2, 353–366. https://doi.org/10.68381/jca18019

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.