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 |
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creator | Lixin, Cheng Shuzhong, Shi 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. |
doi_str_mv | 10.1006/jmaa.1998.6021 |
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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.</description><identifier>ISSN: 0022-247X</identifier><identifier>EISSN: 1096-0813</identifier><identifier>DOI: 10.1006/jmaa.1998.6021</identifier><identifier>CODEN: JMANAK</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>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. 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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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