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Izv. Saratov Univ. Math. Mech. Inform., 2007, Volume 7, Issue 1, Pages 33–39 (Mi isu141)  

Mathematics

Shape-preserving linear n-width of unit balls in $C[0,1]$

S. P. Sidorov

Saratov State University, Chair of Mathematical Economics

Abstract: Let $D^k$, $k$ is a natural number or zero, be the $k$-th differential operator, defined in $C^k(X)$, $X=[0,1]$, and let $C$ be a cone in $C^k(X)$. Let us denote $\delta_n^k(A,C)_{C(X)}:=\inf_{L_n(C)\subset C}\sup_{f\in A}\|D^kf-D^kL_nf\|_{C(X)}$ linear relative $n$-width of set $A\subset C^k(X)$ in $C(X)$ for $D^k$ with constraint $C$. In this paper we estimate linear relative $n$-width of some balls in $C(X)$ for $D^k$ with constraint $C=\{f\in C^k(X):D^kf\ge0\}$.

DOI: https://doi.org/10.18500/1816-9791-2007-7-1-33-39

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UDC: 517.518.85

Citation: S. P. Sidorov, “Shape-preserving linear n-width of unit balls in $C[0,1]$”, Izv. Saratov Univ. Math. Mech. Inform., 7:1 (2007), 33–39

Citation in format AMSBIB
\Bibitem{Sid07}
\by S.~P.~Sidorov
\paper Shape-preserving linear n-width of unit balls in $C[0,1]$
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2007
\vol 7
\issue 1
\pages 33--39
\mathnet{http://mi.mathnet.ru/isu141}
\crossref{https://doi.org/10.18500/1816-9791-2007-7-1-33-39}
\elib{https://elibrary.ru/item.asp?id=9954067}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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