Geodesic
Fréchet-Legendre Functions and Reflexive Banach Spaces
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 915-924 Cet article a éte moissonné depuis la source Heldermann Verlag

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H. H. Bauschke, J. M. Borwein and P. L. Combettes ["Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces", Communications in Contemp. Mathematics 3 (2001) 615--647] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on Rn in a compatible fashion to any Banach space. They were able, among other things, to show that substantial duality results hold for Legendre functions in reflexive spaces. That article focused on essential smoothness in the Gâteaux sense. Our goal herein is to show that similar results hold for Fréchet smoothness and to study related properties of such functions on reflexive Banach spaces.
Classification : 52A41, 46G05, 46N10, 49J50, 90C25
Mots-clés : Convex Function, Legendre function, essentially smooth, essentially strictly convex, Frechet differentiability, Fenchel duality 
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     author = {J. M. Borwein and J. Vanderwerff},
     title = {Fr\'echet-Legendre {Functions} and {Reflexive} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {915--924},
     year = {2010},
     volume = {17},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a11/}
}
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J. M. Borwein; J. Vanderwerff. Fréchet-Legendre Functions and Reflexive Banach Spaces. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 915-924. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a11/