Approximation of Fourier Series of Functions in Besov Space by Borel Means

Authors

  • B. P. Padhy
  • A. Mishra
  • S. Nanda

DOI:

https://doi.org/10.18311/jims/2022/26422

Keywords:

Degree of Approximation, Banach Space, Holder Space, Besov Space, Fourier Series, Borel Mean.

Abstract

In the present article, a result on degree of approximation of Fourier series of functions in the Besov space by Borel mean is established.

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References

G. Das, A. K. Ojha and B. K. Ray, Degree of approximation of functions associated with Hardy-Littlewood series in the Holder metric by Borel Means, J. Math. Anal. Appl., 219, article no. AY975797, (1998), 279–293.

G. H. Hardy, Divergent Series, Oxford University Press, First Edition, 1949.

S. Lal and Shireen, Best approximation of functions of generalized Zygmund class by Matrix-Euler summability mean of Fourier series, Bull. Math. Anal. Appl., 5(4)(2013), 1–13.

F. Moricz and J. Nemeth, Generalized Zygmund classes of functions and strong approximation of Fourier series, Acta. Sci. Math., 73(2007), 637–647.

L. Nayak, G. Das and B. K. Ray, Degree of approximation of Fourier series of functions in Besov space by Defreed Ces‘aro mean, J. Indian Math. Soc., 83(2016), 161–179.

H. K. Nigam, The degree of approximtion by product means, Ultra scientist, 22(3)M(2010), 889–894.

H. K. Nigam, On approximation in generalized Zygmund class, Demonstr. Math. (De Gruyter), 52(2019), 370–387.

H. K. Nigam and M. Hadish, Best approximation of functions in generalized Holder class, J. Inequal. Appl., 2018: 276 (2018), 1–15.

P. Parida, S. K. Paikray, M. Dash and U. K. Misra, Degree of approximation by product (N-,pn,qn)(E,q) summability of Fourier series of a signal belonging to Lip(?,r)-class, TWMS J. App. Engg. Math., 9(4)(2019), 901–908.

S. Prosdor?, Zur Konvergenz der Fourier richen Holder stetiger Funktionen, Math. Nachar, 69(1975), 7–14.

A. D. Ronald and G. Lorentz, Constructive approximation, Springler-Verlag, Berlin, 1993.

M. V. Singh and M. L. Mittal, Approximation of functions in Besov space deferred Cesa`ro mean, J. Inequal Appl., (2016), Article ID: 118.

K. Weierstrass, Uber die analytische sogenannter willkurlicher functionen einer reelen veranderlichen, Verl. d. Kgl. Akad d. Wiss. Berlin, 2(1885), 633–639.

A. Zygmund, Smooth functions, Duke Math. J., 12 (1945), 47–56.

A. Zygmund, Trigonometric Series (Vol.I and II combined), Cambridge University Press, New York, 1993.

Published

2022-08-23

How to Cite

Padhy, B. P., Mishra, A., & Nanda, S. (2022). Approximation of Fourier Series of Functions in Besov Space by Borel Means. The Journal of the Indian Mathematical Society, 89(3-4), 373–385. https://doi.org/10.18311/jims/2022/26422