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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 1 | Year 2016 | Article Id. IJMTT-V36P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P505

Degree of Approximation of functions by their Fourier Series in the Besov space by Generalized Matrix Mean


Madhusmita Mohanty ,Gokulananda Das, Braja Kishore Ray
Abstract

The paper studies the degree of approximation of functions by their Fourier series in the Besov space by matrix mean and this generalizing many known results.

Keywords
Besov space, Holder space, Lipschitz space, matrix method, Fourier series, Modulus of smoothness.
References

[1] Das, G.: Sublinear funcional and a class of Conservative Matrices, Bull. of the Institute of Mathematics Academia Sinica 15(1987) 89-106.
[2] Das, G., Ghosh, T. and Ray, B.K: Degree of Approximation of function by their Fourier series in the generalized Holder metric, proc. Indian Acad. Sci. (Math.Sci) 106(1996) 139-153.
[3] Devore Ronald A. Lorentz, G.: Constructive approximation, Springler- Verlay, Berlin Heidelberg New York, 1993.
[4] King, J.P. : Almost summable sequence, Proc.Amer. Math.Soc.,17(1966) 1219-1225.
[5] Lorentz, G.G. : A contribution to the theory of divergent sequences, Acta Math., 80(1948),167-190.
[6] Prossdorf, S.: Zur Konvergenz der Fourier richen Holder stetiger Funktionen math.Nachar, 69(1975),7-14.
[7] Stieglitz, Fine Verallgemeineinerung des Begriff der Jeponical, 18 (1973) 53-70.
[8] Wojtaszczyk, P.: A Mathematical Introduction to Wevlets, London Mathematical Society students texts 37, Cambridge University Press, New York, 1997.
[9] Zygmund, A .: Smooth fuctions, Duke math. Jounal 12(1945), 47-56.
[10] Zygmund,A.: Trigonometric series vols I & II combined, Cambridge Univ. Press, New York, 1993.

Citation :

Madhusmita Mohanty ,Gokulananda Das, 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 (IJMTT), vol. 36, no. 1, pp. 42-55, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P505

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