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A theorem on absolute summability of Fourier series by Riesz means
Published online by Cambridge University Press: 17 April 2009
Abstract
In 1951 Mohanty established the following theorem.
If Φ(t)log is of bounded variation in (0, π), wherek ≥ πe2and, then is summable, for however large positive Δ. In this present note we have generalised the above theorem by taking a more general type of Riesz means and under the condition, is of bounded variation in (0, π), where c is finite, imposed upon the generating function of Fourier series.
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- Copyright © Australian Mathematical Society 1970