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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257646-4
MathSciNet review:
0257646
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Nörlund 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