RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Sibirsk. Mat. Zh., 2011, Volume 52, Number 6, Pages 1414–1427 (Mi smj2284)

Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$

M. Sh. Shabozova, G. A. Yusupovb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe, Tajikistan
b Tajik National University, Dushanbe, Tajikistan

Abstract: We find the exact values of the $n$-widths for the classes of periodic differentiable functions in $L_2[0,2\pi]$, satisfying the constraint
$$\int_0^ht\widetilde\Omega_m^{1/m}(f^{(r)};t) dt\le\Phi(h),$$
where $h>0$, $m\in\mathbb N$, $r\in\mathbb Z_+$, $\widetilde\Omega_m^{1/m}(f^{(r)};t)$ is the generalized $m$th order continuity modulus of the derivative $f^{(r)}\in L_2[0,2\pi]$, while $\Phi(t)$ is an arbitrary increasing function such that $\Phi(0)=0$.

Keywords: space of square integrable functions, best approximation, extremal characteristic, generalized continuity modulus, width.

Full text: PDF file (343 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2011, 52:6, 1124–1136

Bibliographic databases:

UDC: 517.5
Revised: 10.05.2011

Citation: M. Sh. Shabozov, G. A. Yusupov, “Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$”, Sibirsk. Mat. Zh., 52:6 (2011), 1414–1427; Siberian Math. J., 52:6 (2011), 1124–1136

Citation in format AMSBIB
\Bibitem{ShaYus11} \by M.~Sh.~Shabozov, G.~A.~Yusupov \paper Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in~$L_2$ \jour Sibirsk. Mat. Zh. \yr 2011 \vol 52 \issue 6 \pages 1414--1427 \mathnet{http://mi.mathnet.ru/smj2284} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2961765} \transl \jour Siberian Math. J. \yr 2011 \vol 52 \issue 6 \pages 1124--1136 \crossref{https://doi.org/10.1134/S0037446611060176} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000298650800017} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855170740} 

• http://mi.mathnet.ru/eng/smj2284
• http://mi.mathnet.ru/eng/smj/v52/i6/p1414

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. Tukhliev, “O priblizhenii periodicheskikh funktsii v $L_2$ i znacheniyakh poperechnikov nekotorykh klassov funktsii”, Model. i analiz inform. sistem, 22:1 (2015), 127–143
2. S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Math. Notes, 98:4 (2015), 572–588
3. S. B. Vakarchuk, V. I. Zabutnaya, “Inequalities between Best Polynomial Approximations and Some Smoothness Characteristics in the Space $L_2$ and Widths of Classes of Functions”, Math. Notes, 99:2 (2016), 222–242
4. K. Tukhliev, “Nailuchshie priblizheniya i poperechniki nekotorykh klassov svertok v $L_{2}$”, Tr. IMM UrO RAN, 22, no. 4, 2016, 284–294
5. S. B. Vakarchuk, “Jackson-type inequalities with generalized modulus of continuity and exact values of the $n$-widths for the classes of $(\psi, \beta)$-differentiable functions in $L_2$. I”, Ukr. Math. J., 68:6 (2016), 823–848
6. Vakarchuk S.B., “on the Estimates of Widths of the Classes of Functions Defined By the Generalized Moduli of Continuity and Majorants in the Weighted Space l-2,l-X(0,1)”, Ukr. Math. J., 71:2 (2019), 202–214
7. Babenko V.F., Konareva S.V., “Jackson-Stechkin-Type Inequalities For the Approximation of Elements of Hilbert Spaces”, Ukr. Math. J., 70:9 (2019), 1331–1344
•  Number of views: This page: 232 Full text: 102 References: 38 First page: 6