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Proceedings of the American Mathematical Society

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

 
 

 

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: 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
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