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Description
  • Studujeme epsilon-fréchetovskou diferencovatelnost lipschityovských funkcí na asplundovsky generovaných Banachových prostorech. Dokazujeme větu o střední hodnotě a její ekvivalent, formuli pro vyjádření Clarkeho subdiferenciálu a pomocí tohoto pojmu. Ukazujeme, že v řadě důkazů, kde se používá hluboká Preissova věta o diferencovatelnosti konvexních funkcí, se vystačí se slabším pojmem epsilon-fréchetovské diferencovatelnosti a příslušným lemmate Fabiana a Preisse pro tento pojem platící. Je to ukázáno na argumentech podaných Boreinem, Fitzpatrickem, Gillesem, Scifferem, Benyaminim a Lindenstraussem. (cs)
  • We study the epsilon-Fréchet differentiability of Lipschitz functions on Asplund generated Banach spaces. We prove a mean valued theorem and its equivalent, a formula for Clarke´s subdifferential, in terms of this concept. We inspect proofs of several statements based on the deep Preiss´s theorem on Fréchet differentiability of Lipschitz functions and we recognize that it is enough to use a simpler lemma on epsilon-Fréchet differentiability due to Fabian and Preiss. We do so for generic differentiability results of Giles and Sciffer, for the existence of nearest points of Borwein and Fitzpatrick, etc. We also show that the epsilon-Fréchet differentiability is separably reducible.
  • We study the epsilon-Fréchet differentiability of Lipschitz functions on Asplund generated Banach spaces. We prove a mean valued theorem and its equivalent, a formula for Clarke´s subdifferential, in terms of this concept. We inspect proofs of several statements based on the deep Preiss´s theorem on Fréchet differentiability of Lipschitz functions and we recognize that it is enough to use a simpler lemma on epsilon-Fréchet differentiability due to Fabian and Preiss. We do so for generic differentiability results of Giles and Sciffer, for the existence of nearest points of Borwein and Fitzpatrick, etc. We also show that the epsilon-Fréchet differentiability is separably reducible. (en)
Title
  • Epsilon-Fréchet Differentiability of Lipschitz Functions and Applications
  • Epsilon-Fréchet Differentiability of Lipschitz Functions and Applications (en)
  • Epsilon-fréchetovská diferencovatelnost lipschitzovských funkcí a aplikace (cs)
skos:prefLabel
  • Epsilon-Fréchet Differentiability of Lipschitz Functions and Applications
  • Epsilon-Fréchet Differentiability of Lipschitz Functions and Applications (en)
  • Epsilon-fréchetovská diferencovatelnost lipschitzovských funkcí a aplikace (cs)
skos:notation
  • RIV/67985840:_____/06:00079324!RIV07-AV0-67985840
http://linked.open.../vavai/riv/strany
  • 695;709
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/04/0090), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 4
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 474372
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/06:00079324
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • epsilon-Fréchet differentiability; mean value theorem; local epsilon-support (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [0CD130ABE6F2]
http://linked.open...i/riv/nazevZdroje
  • Journal of Convex Analysis
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 13
http://linked.open...iv/tvurceVysledku
  • Fabian, Marián
  • Wang, X.
  • Loewen, P. D.
http://linked.open...n/vavai/riv/zamer
issn
  • 0944-6532
number of pages
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