On Semiconcavity via the Second Difference

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390811" target="_blank" >RIV/00216208:11320/18:10390811 - 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
On Semiconcavity via the Second Difference
Original language description
Let f be a continuous real function on a convex subset of a Banach space. We study what can be said about the semiconcavity (with a general modulus) of f, if we know that the estimate. Delta(2)(h)(f; x) <= omega(parallel to h parallel to) holds, where. Delta(2)(h)(f; x) = f (x + 2h) - 2f (x + h) + f (x) and omega : [0,infinity) -> [0; infinity) is a nondecreasing function right continuous at 0 with omega(0) = 0. A partial answer to this question was given by P. Cannarsa and C. Sinestrari (2004); we prove versions of their result, which are in a sense best possible. We essentially use methods of A. Marchaud, S. B. Stechkin and others, whose results clarify when the inequality vertical bar Delta(2)(h)(f; x)vertical bar <=omega (parallel to h parallel to) implies that f is a C-1 function (and f ' is uniformly continuous with a corresponding modulus of continuity).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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