Geodesic
On Asplund functions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 121-132

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A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.
Classification : 46B03, 46B20, 46G99, 58C20
Keywords: Fréchet differentiability; convex functions; Asplund spaces 
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Tang, Wee-Kee. On Asplund functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 121-132. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a8/