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A classical Olivier’s theorem and statistical convergence. (English) Zbl 1061.40001
L. Olivier [J. Reine Angew. Math. 2, 31–44 (1827)] proved the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. In this paper, the authors prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept. For details, we refer the reader to the paper.

MSC:
40A05 Convergence and divergence of series and sequences
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References:
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