Absolute summability of Fourier series with factors

Dikshit, H. P.; Kumar, Arun

doi:10.2140/pjm.1975.61.59

Cited by 3 publications

(4 citation statements)

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“…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].…”

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confidence: 76%

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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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confidence: 76%

“…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].…”

supporting

confidence: 63%

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

Kumar¹

1977

Proc. Amer. Math. Soc.

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“…The following lemma is contained in [3]. The sufficiency part of the lemma in a less general form is due to Sunouchi [6].…”

Section: (ϋmentioning

confidence: 99%

Absolute convergence fields of some triangular matrix methods

Kumar¹,

Sahu²

1981

Pacific J. Math.

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“…Dealing with the absolute Norlund summability of Fourier series, Izumi and Izumi [3] proved the following theorem, which is a generalization of theorems due to Bosanquet [f] and Mohanty [6,7] Also see Oikshit [2] for the proofs of these theorems.…”

Section: (21) I [A C O S N T + B S I N N T ) = I a { T )mentioning

confidence: 99%