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
Pages :
12
From page :
389
To page :
400
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
Serial Year :
1998
Journal title :
Journal of Mathematical Analysis and Applications
Record number :
931824
Link To Document :
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