Generic Fréchet Differentiability of Convex Functions Dominated by a Lower Semicontinuous Convex Function

In this paper, an extended real-valued proper lower semicontinuous convex functionfon a Banach space is said to have the Fréchet differentiability property (FDP) if every proper lower semicontinuous convex functiongwithg≤fis Fréchet differentiable on a denseGδsubset of intdomg, the interior of the e...

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Veröffentlicht in:Journal of mathematical analysis and applications 1998-09, Vol.225 (2), p.389-400
Hauptverfasser: Lixin, Cheng, Shuzhong, Shi, Bingwu, Wang, Lee, E.S
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Bingwu, Wang
Lee, E.S
description In this paper, an extended real-valued proper lower semicontinuous convex functionfon a Banach space is said to have the Fréchet differentiability property (FDP) if every proper lower semicontinuous convex functiongwithg≤fis Fréchet differentiable on a denseGδsubset of intdomg, the interior of the effective domain ofg. We show thatfhas the FDP if and only if thew*-closed convex hull of the image of the subdifferential map offhas the Radon–Nikodým 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.
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source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present)
subjects Calculus of variations and optimal control
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
title Generic Fréchet Differentiability of Convex Functions Dominated by a Lower Semicontinuous Convex Function
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