Vol. 41, No. 1, 1972

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Absolute total-effective (N, pn)(c, 1) method

H. P. Dikshit

Vol. 41 (1972), No. 1, 89–98

In the direction of the total-effectiveness of a (N,pn)(C,1) method, results concerning the summability of a Lebesgue Fourier series and its conjugate series by such a method are known. Supporting the observation that generally bounded variation is the property associated with absolute summability in the same way in which continuity is associated with ordinary summability, the absolute total-effectiveness of a (N,pn)(C,1) method is established in the present paper and the corresponding effectiveness of the (C) method is deduced as a particular case.

Mathematical Subject Classification
Primary: 42A28
Received: 3 March 1971
Revised: 2 September 1971
Published: 1 April 1972
H. P. Dikshit