The Absolute Cesàro Summability of some Series Associated with a Fourier Series and its Allied Series

Mohanty, R.

doi:10.1112/jlms/s1-25.1.63

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=^Ei 2 P -V \ ^) Cos Vt Dt \~^Ei\ ^{12 E Te Sin Vt \ Dt1

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Cited by 16 publications

(13 citation statements)

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“…Introduction and the main results* Concerning the \C\-summability of a Fourier series and a corresponding series with factors the following is known ( [1], [8]) 1 .…”

mentioning

confidence: 99%

Absolute summability of Fourier series with factors

Dikshit¹,

Kumar²

1975

Pacific J. Math.

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“…Introduction and the main results* Concerning the \C\-summability of a Fourier series and a corresponding series with factors the following is known ( [1], [8]) 1 .…”

mentioning

confidence: 99%

Absolute summability of Fourier series with factors

Dikshit¹,

Kumar²

1975

Pacific J. Math.

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“…Combining a result due to Bosanquet and Hyslop [1] with a subsequent result due to Mohanty [5], we have the following. Theorem A.…”

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confidence: 88%

Necessary and sufficient type theorem for absolute Nörlund summability of conjugate series

Kumar¹

1977

Proc. Amer. Math. Soc.

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Abstract.Sufficient conditions for |/V,pn\ summability of the conjugate series of Fourier series have been obtained earlier. The author obtains here a set of necessary and sufficient conditions for the result. This improves earlier results and provides a unified version of them.1. Introduction and the main results. In the present paper we shall prove a result which is directly connected with an earlier paper due to Dikshit and Kumar [3]. Unless stated otherwise we shall use throughout this paper the same definitions and notations as used in [3]. We shall also use the following additional notations: S^=1 Bn(t) denotes the conjugate series of ~2™=0A"(t); \p(t) = \{f(x + t) -f(x -t)}; and "BV [a, b]y represents the class of functions of bounded variation over [a, b].Throughout X(t) will denote a positive nondecreasing function; for n = 1,

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“…Clearly there will be extensions of the results of Theorem 9 involving fractional integrals on the right.J On the other hand, the results of f We can include a = -1 in the case k = 1 of (3.1.2) and in (3.1.6). % We mention in this context that Mohanty (21) has considered conditions for the summability \C\ of the series 2 »°-4» and 2 n(X B n . If we consider (3.1.1) and (3.1.2) as involving integrals of order 0, then Mohanty's results are in the same hierarchy with order -1 (with, of course, r = k = 1).…”

Section: =^Ei 2 P -V \ ^) Cos Vt Dt \~^Ei\ ^{12 E Te Sin Vt \ Dtmentioning

confidence: 99%

On the Absolute Summability of a Fourier Series and its Conjugate Series

Flett

1958

Proceedings of the London Mathematical Society

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The Absolute Cesàro Summability of some Series Associated with a Fourier Series and its Allied Series

Cited by 16 publications

References 0 publications

Absolute summability of Fourier series with factors

Absolute summability of Fourier series with factors

Necessary and sufficient type theorem for absolute Nörlund summability of conjugate series

On the Absolute Summability of a Fourier Series and its Conjugate Series

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