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On two summability methods. (English) Zbl 0795.40006

The authors proved that under some conditions the absolute Riesz summability \(| R,p_ n|_ k\) imply the absolute Cesàro summability \(| C,\alpha|_ k\), where \(k\geq 1\) and \(\alpha>0\).

MSC:

40D25 Inclusion and equivalence theorems in summability theory
40F05 Absolute and strong summability
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
40G99 Special methods of summability

References:

[1] KOGBETLIANTZ E.: Sur les séries absolument sommables par la méthode des moyennes arithmétiques. Bull. Sci. Math. 49 (1925), 234-256. · JFM 51.0182.01
[2] FLETT T. M.: On an extension of absolute summability and some theorems of Littlewood and Foley. Proc. London Math. Soc. 7 (1957), 113-141. · Zbl 0109.04402 · doi:10.1112/plms/s3-7.1.113
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