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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the absolute Nörlund summability factors of infinite series

Author: S. R. Singh
Journal: Proc. Amer. Math. Soc. 25 (1970), 684-689
MSC: Primary 42.20
MathSciNet review: 0257646
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Abstract: Taking the start from an earlier result on the absolute harmonic summability factors due to S. N. Lal, we obtain in this paper suitable factors $\{ {\epsilon _n}\}$ so that the series $\sum {{a_n}} {\epsilon _n}$ may be summable $|N,\;{p_n}|$, whenever the series $\sum {{a_n}}$ is summable $|C,\;1|$.

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Keywords: N&#246;rlund means, absolutely summable <!– MATH $(N,\;{p_n})$ –> <IMG WIDTH="74" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$(N,\;{p_n})$">, absolute harmonic summability, summability <!– MATH $|C,\;\alpha |$ –> <IMG WIDTH="59" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img7.gif" ALT="$\vert C,\;\alpha \vert$">, convex sequences, absolute summability factor theorem
Article copyright: © Copyright 1970 American Mathematical Society