Abstract

K.-S. Lau ["Best approximation by closed sets in Banach spaces", J. Approx. Theory 23 (1978) 29–36] considered the notion of "U-convex spaces" (originally called U-spaces) and showed that both uniform convexity and uniform smoothness imply U-convexity. Also U-convex spaces are uniformly non-square and hence super-reflexive. In this paper we introduce local U-convexity. It is shown that there are two possible localization of U-convexity. We derive our results quantitatively, that is, by the properties of modulus functions. Relationship to modulus of (local) uniform convexity is established and its consequences are discussed.

Author information

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

Sudipta Dutta

Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

sudipta@iitk.ac.in

Keywords

  • Locally uniformly convex
  • super-reflexive spaces
  • U-convexity

Mathematics Subject Classification

46B20

References

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Suggested citation

S. Dutta, B.-L. Lin. “Local U-Convexity.” Journal of Convex Analysis 18 (2011), No. 3, 811–821. https://doi.org/10.68381/jca18050

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