Trudy Instituta Matematiki i Mekhaniki UrO RAN
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






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


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 4, Pages 268–278
DOI: https://doi.org/10.21538/0134-4889-2020-26-4-268-278
(Mi timm1781)
 

Upper estimates for best mean-square approximations for some classes of bivariate functions by Fourier-Chebyshev sums

M. Sh. Shabozov, О. А. Jurakhonov

Tajik National University, Dushanbe
References:
Abstract: In space $L_{2,\rho}$ of bivariate functions summable with square on set $Q=[-1,1]^2$ with weight $\rho(x,y)={1}/{\sqrt{(1-x^{2})(1-y^{2})}}$ the sharp inequalities of Jackson–Stechkin type in which the best polynomial approximation estimated above by Peetre $\mathcal{K}$-functional were obtained. We also find the exact values of various widths of classes of functions defined by generalized modulus of continuity and $\mathcal{K}$-functionals. Also the exact upper bounds for modules of coefficients of Fourier — Tchebychev on considered classes of functions were calculated.
Keywords: mean-squared approximation, generalized modulus of continuity, Fourier — Tchebychev double series, translated operator.
Received: 08.08.2020
Revised: 16.11.2020
Accepted: 23.11.2020
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 42A10, 41A17, 41A44
Language: Russian
Citation: M. Sh. Shabozov, О. А. Jurakhonov, “Upper estimates for best mean-square approximations for some classes of bivariate functions by Fourier-Chebyshev sums”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 268–278
Citation in format AMSBIB
\Bibitem{ShaJur20}
\by M.~Sh.~Shabozov, О.~А.~Jurakhonov
\paper Upper estimates for best mean-square approximations for some classes of bivariate functions by Fourier-Chebyshev sums
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 4
\pages 268--278
\mathnet{http://mi.mathnet.ru/timm1781}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-4-268-278}
\elib{https://elibrary.ru/item.asp?id=44314674}
Linking options:
  • https://www.mathnet.ru/eng/timm1781
  • https://www.mathnet.ru/eng/timm/v26/i4/p268
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024