Geodesic
Convex Functions of Legendre Type in General Banach Spaces
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 569-582.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 46B20, 46G05, 49J50, 52A41
Mots-clés : beta-differentiability, essentially smooth, barrier function, Legendre function, strict convexity 
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     author = {J. M. Borwein and J. D. Vanderwerff},
     title = {Convex {Functions} of {Legendre} {Type} in {General} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {569--582},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2001},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a15/}
}
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J. M. Borwein; J. D. Vanderwerff. Convex Functions of Legendre Type in General Banach Spaces. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 569-582. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a15/