On Asplund functions
نویسنده
چکیده
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.
منابع مشابه
φ - regular functions in Asplund spaces
We introduce in the context of Asplund spaces, a new class of φ-regular functions. This new concept generalizes the one of prox-regularity introduced by Poliquin & Rockafellar (2000) in R and extended to Banach spaces by Bernard & Thibault (2004). In particular, the class of φ-regular functions includes all lower semicontinuous convex functions, all lower-C functions, and convexly C−composite f...
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