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Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results

Yıl 2022, Cilt: 5 Sayı: 2, 105 - 118, 15.06.2022

Jorge Bustamante

https://doi.org/10.33205/cma.1063594

Öz

The second and third powers of the Dirichlet kernel are used to construct discrete linear operators for the approximation of continuous periodic functions. An estimate of the rate of convergence is given. Approximation of non-periodic functions are also considered.

Anahtar Kelimeler

Discrete linear operators rate of convergence direct results Dirichlet kernel

Teşekkür

I have not supporting institution

Kaynakça

  • R. Bojanic, O. Shisha: Approximation of continuous, periodic functions by discrete linear positive operators, J. Approximation Theory, 11 (1974), 231–235.
  • J. Bustamante, L. Flores-de-Jesús: Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fejér sums, Constr. Math. Anal., 3 (2) (2020), 53-63.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Academic Press, New-York and London, (1971).
  • P. L. Butzer, R. J. Stens: Chebyshev transform methods in the theory of best algebraic approximation, Abh. Math. Sem. Univ. Hamburg, 45 (1976), 165-190.
  • R. DeVore: The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Mathematics No. 293, Springer-Verlag Berlin / Heidelberg / New York, (1972).
  • S. Foucart, Y. Kryakin and A. Shadrin: On the exact constant in the Jackson-Stechkin inequality for the uniform metric, Constr. Approx., 29 (2009), 157-179.
  • R. B. Saxena, K. B. Srivastava: On interpolation operators (I), Anal. Numér. Théor. Approx., 7 (2) (1978), 211-223.
  • S. B. Stechkin: Order of best approximation of continuous functions (in Russian), Izv. Akad. Nauk SSSR, 15 (3) (1951), 219-242.
  • O. Kis, P. Vértesi: On a new interpolation process (in Russian), Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 10 (1967), 117-128.

Yıl 2022, Cilt: 5 Sayı: 2, 105 - 118, 15.06.2022

Jorge Bustamante

https://doi.org/10.33205/cma.1063594

Öz

Kaynakça

  • R. Bojanic, O. Shisha: Approximation of continuous, periodic functions by discrete linear positive operators, J. Approximation Theory, 11 (1974), 231–235.
  • J. Bustamante, L. Flores-de-Jesús: Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fejér sums, Constr. Math. Anal., 3 (2) (2020), 53-63.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Academic Press, New-York and London, (1971).
  • P. L. Butzer, R. J. Stens: Chebyshev transform methods in the theory of best algebraic approximation, Abh. Math. Sem. Univ. Hamburg, 45 (1976), 165-190.
  • R. DeVore: The Approximation of Continuous Functions by Positive Linear Operators, Lecture Notes in Mathematics No. 293, Springer-Verlag Berlin / Heidelberg / New York, (1972).
  • S. Foucart, Y. Kryakin and A. Shadrin: On the exact constant in the Jackson-Stechkin inequality for the uniform metric, Constr. Approx., 29 (2009), 157-179.
  • R. B. Saxena, K. B. Srivastava: On interpolation operators (I), Anal. Numér. Théor. Approx., 7 (2) (1978), 211-223.
  • S. B. Stechkin: Order of best approximation of continuous functions (in Russian), Izv. Akad. Nauk SSSR, 15 (3) (1951), 219-242.
  • O. Kis, P. Vértesi: On a new interpolation process (in Russian), Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 10 (1967), 117-128.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Jorge Bustamante 0000-0003-2856-6738

Yayımlanma Tarihi 15 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA Bustamante, J. (2022). Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. Constructive Mathematical Analysis, 5(2), 105-118. https://doi.org/10.33205/cma.1063594
AMA Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. Haziran 2022;5(2):105-118. doi:10.33205/cma.1063594
Chicago Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis 5, sy. 2 (Haziran 2022): 105-18. https://doi.org/10.33205/cma.1063594.
EndNote Bustamante J (01 Haziran 2022) Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. Constructive Mathematical Analysis 5 2 105–118.
IEEE J. Bustamante, “Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results”, CMA, c. 5, sy. 2, ss. 105–118, 2022, doi: 10.33205/cma.1063594.
ISNAD Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis 5/2 (Haziran 2022), 105-118. https://doi.org/10.33205/cma.1063594.
JAMA Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. 2022;5:105–118.
MLA Bustamante, Jorge. “Power of Dirichlet Kernels and Approximation by Discrete Linear Operators $\textit{I}$: Direct Results”. Constructive Mathematical Analysis, c. 5, sy. 2, 2022, ss. 105-18, doi:10.33205/cma.1063594.
Vancouver Bustamante J. Power of Dirichlet kernels and approximation by discrete linear operators $\textit{I}$: direct results. CMA. 2022;5(2):105-18.
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