Approximation Theory on Summability of Fourier Series

Authors

  • Sanjay Mukherjee Research Scholor, MATS University, Raipur(C.G.), India
  • A J Khan MATS University, Raipur(C.G.), India

Keywords:

Fourier series, Borel means, Lebesgue series.

Abstract

The results of Chandra to (e,c) means U.K.Shrivastava and S.K.Verma have proved the following theorem

THEOREM : Let . Then

,

Where  is nth (e, c) means of fourier series of f at x.     

In this paper we obtain the Fourier series by (N,p,q)(E,1) which is the analogues  to  the (e , c) means given above .The theorem is as follows

THEOREM: Let  and  be the positive monotonic, non increasing sequence of real numbers be summable (N,p,q)(E,1) to f(x) at the point t=x is

                  

References

G.H. Hardy, Divergent series, Oxford University Press, Oxford,UK,1st edition ,1949.

D. Borwein , On product of sequences ,Journal of the London Mathematical Society, vol.33pp.352-357, (1958).

A. Zygmund , Trigonometric Series. Vol. I Cambridge University Press, Cambridge, UK, 2nd edition, 1959.

P. Chandra. On the degree of approximation of function belonging to Lipschitz Class. Labdev. Jour. Science and Technology, 13A (1975), 181-183.

P. Chandra. On the degree of approximation of continuous functions Commun. Fac. Sci. Univ. Ankara Ser A, 30(1981),7-16.

K.Ikeno, Lebesgue constant for a family of Summability method, Tohoku Math. J.,17(1965),250-265. [7] B.Kuttner, C.T.Rjajagopal, and M.S.Rangachari, Tauberian convergence theorems for summability methods of the Karamata family, J.Indian Math. Soc. 44(1980),23-38.

A.Meir, Tauberian constants for a family of transformations, Annals of Math. 78(1963), 594-599

U.K.Shrivastava and S.L.Varma, On the degree of approximation of function belonging to Lipschitz Class by (e,c) means, Tamkang Journal of Maths, 26,no.3(1965),97-101.

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Published

2019-04-09

How to Cite

Mukherjee, S., & J Khan, A. (2019). Approximation Theory on Summability of Fourier Series. American Scientific Research Journal for Engineering, Technology, and Sciences, 54(1), 131–136. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/4764

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