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On the relation of generalized Valiron summability to Cesàro summability
Proceedings of the Indian Academy of Sciences - Section A, 1981A family (Vak) of summability methods, called generalized Valiron summability, is defined. The well-known summability methods (Bα,γ), (Eρ, (Tα), (Sβ) and (Va) are members of this family. In §3 some properties of the (Bα,γ) and (Vak) transforms are established.
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On Strong Summability of Fourier Series of Summable Functions
Ukrainian Mathematical Journal, 2000Summary: In the metric of \(L\) we obtain estimates for the generalized means of deviations of partial Fourier sums from an arbitrary summable function in terms of the corresponding means of its best approximations by trigonometric polynomials.
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On generalized |A|k-summability factors [PDF]
Computers and Mathematics With Applications, 2010 The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Rhoades and Savas [B. Rhoades, E.
Savaş, Ekrem
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On Ingham summability and summability by Lambert series
Mathematical Proceedings of the Cambridge Philosophical Society, 1955In his paper ‘Some Tauberian theorems connected with the prime number theorem’, Ingham(10) discusses the method of summation of the series defined ...
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The Distribution of Sequences and Summability
Canadian Journal of Mathematics, 1963We suppose that 0 <sn≤ 1 for everyn, and denote byn(α, β) the number ofS0, S1,S2, . . . ,Snwhich fall in the interval 0 ≤ α <x≤ β ≤ 1. If there exists a functiong(t), 0 ≤t≤ 1, such thatfor every interval (α, β] with 0 ≤ β — α ≤ 1, the sequence (Sn) is said to have a distribution functiong(t), 0 ≤t≤ 1, in the interval [0, 1], (see 9, p. 87).
Dowidar, A. F., Petersen, G. M.
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Summability factors for generalized absolute summability. II
2001Summary: A new theorem concerning the characterization of absolute summability factors has been proved. [For Part I and III see ibid. 31--39 (2001; Zbl 1078.40501) and 47--52 (2001; Zbl 1078.40502).]
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On the relation of Cesàro summability to generalized (F α, q) summability
Proceedings of the Indian Academy of Sciences - Section A, 1976Standard special cases of the sequence-to-functionF (a, q)-transform of Meir4 admit of a more general, essentially more refined, characterization as theFk (a, q)-transform of the sequel, adapted from one of Faulhaber’s.1 The theorem proved,viz., that (Fa, qk) summability for sequences, corresponding to the latter transform, includes Cesaro summability ...
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On Riesz Summability and Summability by Dirichlet's Series
American Journal of Mathematics, 1947openaire +1 more source