Journal of Convex Analysis 08 (2001), No. 2, 569--582
Copyright Heldermann Verlag 2001
Convex Functions of Legendre Type in General Banach Spaces
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.
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 is given.
Keywords: beta-differentiability, essentially smooth, barrier function, Legendre function, strict convexity.
MSC: 46B20; 46G05, 49J50, 52A41.
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