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  • Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions.
  • Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. Singular points of order $k$ of $f$ are those points at which the Clarke subdifferential of $f$ is at least $k$-dimensional. We prove that if $f$ is Clarke regu lar, then the set of all singular points of order $k$ of $f$ can be covered by countably many Lipchitz surfaces of codimension $k$. We prove also two results on arbitrary functions, which work with Hadamard directional derivatives and can be considered as generalization of the above result on Clarke regular functions. (en)
Title
  • Singular points of order k of Clarke regular and arbitrary functions
  • Singular points of order k of Clarke regular and arbitrary functions (en)
skos:prefLabel
  • Singular points of order k of Clarke regular and arbitrary functions
  • Singular points of order k of Clarke regular and arbitrary functions (en)
skos:notation
  • RIV/00216208:11320/12:10127428!RIV13-GA0-11320___
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  • P(GA201/09/0067), Z(MSM0021620839)
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  • 1
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  • 168147
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  • RIV/00216208:11320/12:10127428
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  • Hadamard derivative; singularities; Clarke regular functions (en)
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  • CZ - Česká republika
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  • [13B9CF2B1E8A]
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  • Commentationes Mathematicae Universitatis Carolinae
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  • 53
http://linked.open...iv/tvurceVysledku
  • Zajíček, Luděk
http://linked.open...n/vavai/riv/zamer
issn
  • 0010-2628
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  • 11320
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