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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10127167" target="_blank" >RIV/00216208:11320/12:10127167 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language description

We prove that a locally Lipschitz function on an open subset G of an Asplund space X, whose restrictions to "many lines" are essentially smooth (i.e., almost everywhere strictly differentiable), is generically Frechet differentiable on X. In this way weobtain 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 somenew 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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F09%2F0067" target="_blank" >GA201/09/0067: Theory of real functions and descriptive set theory II</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

19

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

26

Pages from-to

23-48

UT code for WoS article

000301551300002

EID of the result in the Scopus database

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