Geodesic
Convex Functions of Legendre Type in General Banach Spaces
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 569-582 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
@article{JCA_2001_8_2_JCA_2001_8_2_a15,
     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},
     year = {2001},
     volume = {8},
     number = {2},
     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/