Generic Frechet differentiability of convex functions dominated by a lower semicontinuous convex function

摘要

In this paper, an extended real-valued proper lower semicontinuous convex function f on a Banach space is said to have the Frechet differentiability property (FDP) if every proper lower semicontinuous convex function g with g less than or equal to f is Frechet differentiable on a dense G(delta), subset of int dom g, the interior of the effective domain of g. We show that f has the FDP if and only if the w*-closed convex hull of the image of the subdifferential map of f has the Radon-Nikodym property. This is a generalization of the main theorem in a paper by Lixin and Shuzhong (to appear). According to this result, it also gives several new criteria of Asplund spaces, (C) 1998 Academic Press. [References: 14]