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

Authors

  • N. A. Davydov

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.

Published

25.06.1995

Issue

Section

Research articles

How to Cite

Davydov, N. A. “On Necessary and Sufficient Conditions for the Summability of a Numerical Series to Imply Its Convergence”. Ukrains’kyi Matematychnyi Zhurnal, vol. 47, no. 6, June 1995, pp. 747–754, https://umj.imath.kiev.ua/index.php/umj/article/view/5467.