Çanak, Ịbrahim; Erdem, Yılmaz; Totur, Ümit Some Tauberian theorems for (A)\((C,\alpha )\) summability method. (English) Zbl 1202.40007 Math. Comput. Modelling 52, No. 5-6, 738-743 (2010). Summary: We give some Tauberian conditions in order to obtain \((C,\alpha )\) summability from \((A)(C,\alpha )\) summability. Cited in 7 Documents MSC: 40G05 Cesàro, Euler, Nörlund and Hausdorff methods 40E05 Tauberian theorems 40G10 Abel, Borel and power series methods Keywords:Abel summability; Cesáro summability; Tauberian conditions; Tauberian theorems PDFBibTeX XMLCite \textit{Ị. Çanak} et al., Math. Comput. Modelling 52, No. 5--6, 738--743 (2010; Zbl 1202.40007) Full Text: DOI References: [1] Hardy, G. H., Divergent Series (1991), Chelsea: Chelsea New York, NY · Zbl 0897.01044 [2] Abel, N. H., Recherches sur la série \(1 + \frac{m}{1} x + \frac{m(m - 1)}{1.2} x^2 + \cdots \), J. für Math., 1, 311-339 (1826) · ERAM 001.0031cj [3] Tauber, A., Ein satz der Theorie der unendlichen Reihen, Monatsh. f. Math., 8, 273-277 (1897) · JFM 28.0221.02 [4] Littlewood, J. E., The converse of Abel’s theorem on power series, Proc. Lond. Math. Soc., 9, 2, 434-448 (1911) · JFM 42.0276.01 [5] Hardy, G. H.; Littlewood, J. E., Tauberian theorems concerning power and Dirichlet’s series whose coefficients are positive, Proc. Lond. Math. Soc., 13, 2, 174-191 (1913) · JFM 45.0389.02 [6] Szàsz, O., Generalization of two theorems of Hardy and Littlewood on power series, Duke Math. J., 1, 105-111 (1935) · JFM 61.0217.03 [7] Dik, M., Tauberian theorems for sequences with moderately oscillatory control modulo, Math. Morav., 5, 57-94 (2001) · Zbl 1046.40004 [8] Pati, T., On tauberian theorems, (Rath, D.; Nanda, S., Sequences, Summability and Fourier Analysis (2005), Narosa Publishing House), 84-96 [9] Kogbetliantz, E., Sur le séries absolument sommables par la méthode des moyennes arihtmétiques, Bull. Soc. Math., 49, 2, 234-251 (1925) · JFM 51.0182.01 [10] Kogbetliantz, E., Sommation des séries et intégrals divergents par les moyennes arithmétiques et typiques, Memorial Sci. Math., 51, 1-84 (1931) · JFM 57.1376.02 [11] Hardy, G. H., Theorems relating to the summability and convergence of slowly oscillating series, Proc. Lond. Math. Soc., 8, 2, 301-320 (1910) · JFM 41.0278.02 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.