Title of article :
Generic Fr´echet Differentiability of Convex
Functions Dominated by a Lower
Semicontinuous Convex Function
Author/Authors :
Cheng Lixin، نويسنده , , Cheng Lixin and Shi Shuzhong، نويسنده , , and Wang Bingwu، نويسنده , , E. S. LeeU، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 1998
Abstract :
In this paper, an extended real-valued proper lower semicontinuous convex
function f on a Banach space is said to have the Fr´echet differentiability property
FDP.if every proper lower semicontinuous convex function g with gFf is
Fr´echet differentiable on a dense G subset of int dom g, the interior of the d
effective domain of g. We show that f has the FDP if and only if the wU-closed
convex hull of the image of the subdifferential map of f has the Radon]Nikod´ym
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.
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications