Degree of Approximation of Functions in Besov Space by Eular Means of Fourier Series

Varsha Karanjgaokar; Snehal Rahatgaonkar

doi:https://doi.org/10.14445/22315373/IJMTT-V71I6P108

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 6 | Year 2025 | Article Id. IJMTT-V71I6P108 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I6P108

Degree of Approximation of Functions in Besov Space by Eular Means of Fourier Series

Varsha Karanjgaokar, Snehal Rahatgaonkar

Received	Revised	Accepted	Published
18 Apr 2025	30 May 2025	18 Jun 2025	30 Jun 2025

Abstract

In this paper, we established a result on the degree of approximation of functions in the Besov Space by Eular means of trigonometric Fourier series.

Keywords

Besov space, Degree of Approximation, Eular Summability, Periodic functions, Trigonometric Fourier Series. Subject Classification Number : 30H25, 42A10, 41A10, 41A25, 42A24.

References

[1] A. Zygmund, “Smooth Fuctions,” Duke math. Journal, vol. 12, no. 1, pp. 47-56, 1945.
[CrossRef] [Google Scholar] [Publisher Link]
[2] Antoni Zygmund, Trigonometric Series, Cambridge University Press, vol. 1, 2002.
[Google Scholar] [Publisher Link]
[3] Ronald A. DeVore, and George G. Lorentz, Constructive Approximation, Springer Science Business Media, 1993.
[Google Scholar] [Publisher Link]
[4] Madhusmita Mohanty, Gokulananda Das, and Braja Kishore Ray, “Degree of Approximation of Functions by Their Fourier Series in the Besov Space by Generalized Matrix Mean,” International Journal of Mathematics Trends and Technology, vol. 36, no. 1, pp. 42-62, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Prem Chandra, “Degree of Approximation of Functions in the Hölder Metric,” The Journal of the Indian mathematical Society, vol. 53, no. 1-4, pp. 99-114, 1988.
[Google Scholar]
[6] P. Chandra, “𝐿𝑝 Approximation of Function by Euler Means,” The Journal of Mathematical Sciences, vol. 1, New series, 27-34, 2002.
[7] P. Chandra, and R.N. Mohapatra, “Degree of Approximation of Functions in the Hölder Metric,” Acta Mathematica Hungarica, vol. 41 , 67-76, 1983.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Siegfried Prössdorf, “On the Convergence of Fourier Series of Hölder Continuous Functions,” Mathematische Nachrichten, vol. 69, no. 1, pp. 7-14, 1975.
[CrossRef] [Google Scholar] [Publisher Link]
[9] T. Singh, “Approximation to Continuous in the Holder Metric,” Matematički Vesnik, vol. 43, pp. 111-118, 1991.
[10] Przemyslaw Wojtaszczyk, A Mathematical Introduction to Wavelets, Cambridge University Press, 1997.
[Google Scholar] [Publisher Link]
[11] Xhevat Z. Krasniqi, and Bogdan Szal, “On the Degree of Approximation of Continuous Functions by Means of Fourier Series in the Hölder Metric,” Analysis in Theory and Applications, vol. 35, no. 4, pp. 392-404, 2019.
[Google Scholar] [Publisher Link]

Citation :

Varsha Karanjgaokar, Snehal Rahatgaonkar, "Degree of Approximation of Functions in Besov Space by Eular Means of Fourier Series," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 6, pp. 81-91, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I6P108