About: Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We prove that a locally Lipschitz function on an open subset G of an Asplund space X, whose restrictions to %22many lines%22 are essentially smooth (i.e., almost everywhere strictly differentiable), is generically Frechet differentiable on X. In this way we obtain new proofs of known Frechet differentiability properties of approximately convex functions, Lipschitz regular functions, saddle (or biconvex) Lipschitz functions, and essentially smooth functions (in the sense of Borwein and Moors), and also some new differentiability results (e.g., for partially DC functions). We show that classes of functions S-e(g)(G) and R-e(g)(G) (defined via linear essential smoothness) are respectively larger than classes S-e(G) (of essentially smooth functions) and R-e(G) studied by Borwein and Moors, and have also nice properties. In particular, we prove that members of S-e(g)(G) are uniquely determined by their Clarke subdifferentials. We also show the inclusion S-e(G) subset of R-e(G) for Borwein-Moors classes. We prove that a locally Lipschitz function on an open subset G of an Asplund space X, whose restrictions to %22many lines%22 are essentially smooth (i.e., almost everywhere strictly differentiable), is generically Frechet differentiable on X. In this way we obtain new proofs of known Frechet differentiability properties of approximately convex functions, Lipschitz regular functions, saddle (or biconvex) Lipschitz functions, and essentially smooth functions (in the sense of Borwein and Moors), and also some new differentiability results (e.g., for partially DC functions). We show that classes of functions S-e(g)(G) and R-e(g)(G) (defined via linear essential smoothness) are respectively larger than classes S-e(G) (of essentially smooth functions) and R-e(G) studied by Borwein and Moors, and have also nice properties. In particular, we prove that members of S-e(g)(G) are uniquely determined by their Clarke subdifferentials. We also show the inclusion S-e(G) subset of R-e(G) for Borwein-Moors classes. (en)
Title	Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines (en)
skos:prefLabel	Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines Generic Frechet Differentiability on Asplund Spaces via A.E. Strict Differentiability on Many Lines (en)
skos:notation	RIV/00216208:11320/12:10127167!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita	I P Z
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0067), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Zajíček, Luděk
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	137875
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10127167
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	separable reduction; essentially smooth functions; Generic Frechet differentiability (en)
http://linked.open.../riv/klicoveSlovo	Generic Frechet differentiability essentially smooth functions separable reduction
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[9D43A5426E95]
http://linked.open...i/riv/nazevZdroje	Journal of Convex Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Theory of real functions and descriptive set theory II
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	19
http://linked.open...iv/tvurceVysledku	Zajíček, Luděk
http://linked.open...ain/vavai/riv/wos	000301551300002
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0944-6532
number of pages	26 (xsd:int)
http://localhost/t...ganizacniJednotka	11320

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