Abstract

Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of the existence of "universal" barriers on arbitrary open convex sets in Rn\mathbb{R}^n is given.

Author information

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

Jonathan M. Borwein

Dept. of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada

J. D. Vanderwerff

Dept. of Mathematics, La Sierra University, Riverside, CA 92515, U.S.A.

Keywords

  • beta-differentiability
  • essentially smooth
  • barrier function
  • Legendre function
  • strict convexity

Mathematics Subject Classification

46B20; 46G05, 49J50, 52A41

Suggested citation

J. M. Borwein, J. D. Vanderwerff. “Convex Functions of Legendre Type in General Banach Spaces.” Journal of Convex Analysis 8 (2001), No. 2, 569–581. https://doi.org/10.68381/jca08030

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press.