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Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences. (English) Zbl 1051.40006

The author proves two interesting theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences. E.g. it is proved that if a slowly decreasing sequence \(\{x_k\}\) of real numbers is statistically harmonic summable then it is convergent in the ordinary sense. Several new lemmas having interest in themselves are used in the proofs.

MSC:

40E05 Tauberian theorems
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
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