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Matematicheskie Zametki, 1998, Volume 63, Issue 3, Pages 332–342
DOI: https://doi.org/10.4213/mzm1287
(Mi mzm1287)
 

This article is cited in 2 scientific papers (total in 2 papers)

Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces

V. F. Babenko, V. A. Kofanov, S. A. Pichugov

Dnepropetrovsk State University
Full-text PDF (233 kB) Citations (2)
References:
Abstract: Suppose that $X$ and $Y$ are real Banach spaces, $U\subset X$ is an open bounded set star-shaped with respect to some point, $n,k\in\mathbb N$, $k<n$, and $M_{n,k}(U,Y)$ is the sharp constant in the Markov type inequality for derivatives of polynomial mappings. It is proved that for any $M\ge M_{n,k}(U,Y)$ there exists a constant $B>0$ such that for any function$f\in C^n(U,Y)$ the following inequality holds:
$$ |\kern -.8pt|\kern -.8pt|f^{(k)}|\kern -.8pt|\kern -.8pt|_U\le M|\kern -.8pt|\kern -.8pt|f|\kern -.8pt|\kern -.8pt|_U+B|\kern -.8pt|\kern -.8pt|f^{(n)}|\kern -.8pt|\kern -.8pt|_U. $$
The constant $M=M_{n-1,k}(U,Y)$ is best possible in the sense that $M_{n-1,k}(U,Y)=\inf M$, where $\inf$ is taken over all $M$ such that for some $B>0$ the estimate holds for all $f\in C^n(U,Y)$.
Received: 17.10.1995
Revised: 29.07.1997
English version:
Mathematical Notes, 1998, Volume 63, Issue 3, Pages 293–301
DOI: https://doi.org/10.1007/BF02317773
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. F. Babenko, V. A. Kofanov, S. A. Pichugov, “Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces”, Mat. Zametki, 63:3 (1998), 332–342; Math. Notes, 63:3 (1998), 293–301
Citation in format AMSBIB
\Bibitem{BabKofPic98}
\by V.~F.~Babenko, V.~A.~Kofanov, S.~A.~Pichugov
\paper Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 332--342
\mathnet{http://mi.mathnet.ru/mzm1287}
\crossref{https://doi.org/10.4213/mzm1287}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1631920}
\zmath{https://zbmath.org/?q=an:0927.46025}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 293--301
\crossref{https://doi.org/10.1007/BF02317773}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075783100002}
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  • https://www.mathnet.ru/eng/mzm/v63/i3/p332
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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