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On two summability methods

  • Hüseyin Bor (a1)

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Let Σan be a given infinite series with partial sums sn, and rn = nan. By and we denote the nth Cesáro means of order α (α –1) of the sequences (sn) and (rn), respectively. The series Σan is said to be absolutely summable (C, a) with index k, or simply summable |C, α|k, k ≥ 1, if

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[1]Bor, H.. On ssummability factors of infinite series. J. Univ. Kuwait Sci. 10 (1983), 3742.
[2]Flett, T. M.. On an extension of absolute summability and theorems of Littlewood and Paley. Proc. Lond. Math. Soc. 7 (1957), 113141.
[3]Kogbetliantz, E.. Sur les séries absolument sommables par la méthode des moyennea arithmétiques. Bull. Sci. Math. 49 (1925), 234256.
[4]Maddox, I. J.. Introductory Mathematical Analysis (Adam Hilger, 1977).

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