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



Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2013, Volume 13, Issue 1(1), Pages 45–49 (Mi isu351)  

This article is cited in 6 scientific papers (total in 6 papers)

Mathematics

Approximation of Smooth Functions in $L^{p(x)}_{2\pi}$ by Vallee-Poussin Means

I. I. Sharapudinov

Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala

Abstract: Variable exponent $p(x)$ Lebesgue spaces $L^{p(x)}_{2\pi}$ is considered. For $f\in L^{p(x)}_{2\pi}$ Vallee–Poussin means $V_m^n(f,x)$ can be defined as $V_m^n(f,x)=\frac{1}{m+1}\sum\limits_{l=0}^mS_{n+l}(f,x),$ where $S_{k}(f,x)$ — partial Fourier sum of $f(x)$ of order $k$. Approximative properties of operators $V_m^n(f)=V_m^n(f,x)$ are investigated in $L^{p(x)}_{2\pi}$. Let $p(x)\ge1$ be $2\pi$-periodical variable exponent that satisfies Dini–Lipschitz condition. When $m=n-1$ and $m=n$ the following estimate is proved: $\|f-V_m^n(f)\|_{p(\cdot)}\le \frac{c_r(p)}{n^r}E_n(f^{(r)})_{p(\cdot)}$, where $E_n(f^{(r)})_{p(\cdot)}$ is the best approximation of function $f^{(r)}(x)$ by trigonometric polynomials of order $n$ in $L^{p(x)}_{2\pi}$.

Key words: variable exponent Lebesgue and Sobolev spaces, approximation by trigonometric polynomials, Vallee–Poussin means.

Full text: PDF file (145 kB)
References: PDF file   HTML file

UDC: 517.587

Citation: I. I. Sharapudinov, “Approximation of Smooth Functions in $L^{p(x)}_{2\pi}$ by Vallee-Poussin Means”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:1(1) (2013), 45–49

Citation in format AMSBIB
\Bibitem{Sha13}
\by I.~I.~Sharapudinov
\paper Approximation of Smooth Functions in $L^{p(x)}_{2\pi}$ by Vallee-Poussin Means
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 1(1)
\pages 45--49
\mathnet{http://mi.mathnet.ru/isu351}


Linking options:
  • http://mi.mathnet.ru/eng/isu351
  • http://mi.mathnet.ru/eng/isu/v13/i1/p45

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. I. I. Sharapudinov, “Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by finite Fourier-Haar series”, Sb. Math., 205:2 (2014), 291–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. I. I. Sharapudinov, “Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by de la Vallée-Poussin means”, Sb. Math., 207:7 (2016), 1010–1036  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. M. G. Magomed-Kasumov, “Approximation Properties of de la Vallée-Poussin Means for Piecewise Smooth Functions”, Math. Notes, 100:2 (2016), 229–244  mathnet  crossref  crossref  mathscinet  isi  elib
    4. S. S. Volosivets, “Approximation of functions and their conjugates in variable Lebesgue spaces”, Sb. Math., 208:1 (2017), 44–59  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. I. I. Sharapudinov, “Perekryvayuschie preobrazovaniya dlya priblizheniya nepreryvnykh funktsii posredstvom povtornykh srednikh Valle Pussena”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 70–92  mathnet  crossref
    6. I. I. Sharapudinov, T. I. Sharapudinov, M. G. Magomed-Kasumov, “Approksimativnye svoistva povtornykh srednikh Valle-Pussena dlya kusochno gladkikh funktsii”, Sib. matem. zhurn., 60:3 (2019), 695–713  mathnet  crossref
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
    Number of views:
    This page:283
    Full text:106
    References:39

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019