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

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 292–308 (Mi timm1251)

Jackson — Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions

M. Sh. Shabozova, K.Tukhlievb

a Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
b Khujand State University

Abstract: In the Hilbert space $L_{2,\mu}[-1,1]$ with Chebyshev weight $\mu(x):=1/\sqrt{1-x^{2}}$, we obtain Jackson–Stechkin type inequalities between the value $E_{n-1}(f)_{L_{2,\mu}}$ of the best approximation of a function $f(x)$ by algebraic polynomials of degree at most $n-1$ and the $m$th-order generalized modulus of continuity $\Omega_{m}({\mathcal D}^{r}f;t)$, where ${\mathcal D}$ is some second-order differential operator. For classes of functions $W^{(2r)}_{p,m}(\Psi)$ ($m,r\in\mathbb{N}$, $1/(2r)$<$p\le2$) defined by the mentioned modulus of continuity and a given majorant $\Psi(t)$ ($t\ge0$), which satisfies certain constraints, we calculate the values of various $n$-widths in the space $L_{2,\mu}[-1,1]$.

Keywords: best approximation, Chebyshev polynomials, generalized modulus of continuity of $m$th order, Chebyshev — Fourier coefficients, $n$-widths.

Full text: PDF file (237 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.5

Citation: M. Sh. Shabozov, K.Tukhliev, “Jackson — Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 292–308

Citation in format AMSBIB
\Bibitem{ShaTuk15} \by M.~Sh.~Shabozov, K.Tukhliev \paper Jackson --- Stechkin type inequalities with generalized moduli of continuity and widths of some classes of functions \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2015 \vol 21 \issue 4 \pages 292--308 \mathnet{http://mi.mathnet.ru/timm1251} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468452} \elib{https://elibrary.ru/item.asp?id=25301007} 

• http://mi.mathnet.ru/eng/timm1251
• http://mi.mathnet.ru/eng/timm/v21/i4/p292

 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, “Srednekvadraticheskoe priblizhenie funktsii ryadami Fure–Besselya i znacheniya poperechnikov nekotorykh funktsionalnykh klassov”, Chebyshevskii sb., 17:4 (2016), 141–156
2. Mukim S. Saidusajnov, “$\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space”, Ural Math. J., 3:2 (2017), 74–81
3. M. Sh. Shabozov, M. S. Saidusajnov, “Upper Bounds for the Approximation of Certain Classes of Functions of a Complex Variable by Fourier Series in the Space $L_2$ and $n$-Widths”, Math. Notes, 103:4 (2018), 656–668
4. O. A. Dzhurakhonov, “Priblizhenie funktsii dvukh peremennykh «krugovymi» summami Fure — Chebysheva v $L_{2,\rho}$”, Vladikavk. matem. zhurn., 22:2 (2020), 5–17
•  Number of views: This page: 261 Full text: 66 References: 56 First page: 28