Abstract

We present some geometric and approximation theoretic characterizations of locally uniform convex, compactly locally uniformly convex, nearly uniformly convex, compactly uniformly convex and uniformly convex Banach spaces. The approximation theoretic characterizations of compactly locally uniformly convex spaces presented in this paper provide some answers to a question posed by F. Deutsch and J. Lambert in their paper On continuity of metric projections, J. Approx. Theory 29 (1980) 116–131.

Author information

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

P. Shunmugaraj

Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India

psraj@iitk.ac.in

Vamsinadh Thota

Dept. of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India

vamst@iitk.ac.in

Keywords

  • Compactly locally uniformly convex
  • nearly uniformly convex
  • compactly uniformly convex
  • approximative compactness
  • metric projection

Mathematics Subject Classification

41A65, 46B20

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Suggested citation

P. Shunmugaraj, V. Thota. “Some Geometric and Proximinality Properties in Banach Spaces.” Journal of Convex Analysis 25 (2018), No. 4, 1139–1158. https://doi.org/10.68381/jca25072

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.