Approximation Theory on Summability of Fourier 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
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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.352357, (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), 181183.
P. Chandra. On the degree of approximation of continuous functions Commun. Fac. Sci. Univ. Ankara Ser A, 30(1981),716.
K.Ikeno, Lebesgue constant for a family of Summability method, Tohoku Math. J.,17(1965),250265. [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),2338.
A.Meir, Tauberian constants for a family of transformations, Annals of Math. 78(1963), 594599
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),97101.
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