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On necessary and sufficient conditions for the summability of a numerical series to imply its convergence

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Ukrainian Mathematical Journal Aims and scope

Abstract

On the basis of the concepts of (C) -point and (¯R, p)-point of a sequence of complex numbers introduced by the author and results established earlier, we formulate necessary and sufficient conditions for the summability of a number series by a positive Cesaro method or the Riesz method to imply the convergence of this series. We also present a sufficient condition for summability to imply the convergence of a subsequence of its partial sums.

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References

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Authors and Affiliations

  1. Kiev Pedagogical Institute, USSR

    N. A. Davydov

Authors
  1. N. A. Davydov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 747–754, June, 1995.

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Davydov, N.A. On necessary and sufficient conditions for the summability of a numerical series to imply its convergence. Ukr Math J 47, 860–868 (1995). https://doi.org/10.1007/BF01058776

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  • DOI: https://doi.org/10.1007/BF01058776

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