Vol. 33, No. 3, 1970

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On a class of Nörlund means and Fourier series

H. P. Dikshit

Vol. 33 (1970), No. 3, 559–569

By considering a class of Nörlund means that covers as a subclass the corresponding (C) means, we obtain in the present paper, several results concerning absolute Nörlund summability and deduce from these the corresponding |C| results as special cases. What is indeed remarkable, is that a special case of our Theorem 2 improves an earlier result due to Bosanquet and Hyslop in dropping one of the two independent conditions used by them. Further, the proofs of some of our results are shorter and even more direct than the proofs given for the corresponding special cases by using equivalent Riesz means instead of (C) means.

Mathematical Subject Classification
Primary: 42.20
Received: 22 October 1969
Published: 1 June 1970
H. P. Dikshit