Geodesic
A Definition for Strong Rieszian Summability and its Relationship to Strong Cesaro Summability
Glasgow mathematical journal, Tome 1 (1952) no. 2, pp. 94-99

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. Given a series we define , by the relationsThe series Σan is said to be summable (C, k) to the sum s, ifas n→∞, and strongly summable (C, k), k>0, with index p, to the sum s, or summable [C; k, p] to the sum s, if 
Boyd, A. V.; Hyslop, J. M. A Definition for Strong Rieszian Summability and its Relationship to Strong Cesaro Summability. Glasgow mathematical journal, Tome 1 (1952) no. 2, pp. 94-99. doi: 10.1017/S2040618500035516
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[*] * Hyslop, J. M., Proc., Glasgow Math. Assoc., I., p. 16.Google Scholar

[†] † See Lemma 2 below.

[*] * Hardy, G. H. and Riesz, M., The General Theory of Dirichlet Series (Cambridge Tract, No. 18), 27.Google Scholar

[†] † See, for example, Hyslop, J. M., Proc. Edinburgh Math. Soc., (2), 5 (1937), 46–54.CrossRefGoogle Scholar

[‡] ‡ Kogbetliantz, E., Bull, des Sciences Math., (2), 49 (1925), 234–56.Google Scholar

[§] § Hyslop, J. M., loc. cit.Google Scholar

[*] * Hardy, G. H. and Riesz, M., The General Theory of Dirichlet Series (Cambridge Tract, No. 18), 27.Google Scholar

[†] † See, for example, Hyslop, J. M., Proc. Edinburgh Math. Soc., (2), 5 (1937), 46–54.CrossRefGoogle Scholar

[‡] ‡ Kogbetliantz, E., Bull, des Sciences Math., (2), 49 (1925), 234–56.Google Scholar

[§] § Hyslop, J. M., loc. cit.Google Scholar

[*] * Hobson, E. W., The Theory of Functions of a Real Variable, II (1926), 93.Google Scholar

[*] * The term v = 0 in each of the preceding expressions is, of course, zero, and may therefore be omitted.

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