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Zbl 0756.40006
Sulaiman, W.T.
On some summability factors of infinite series.
(English)
[J] Proc. Am. Math. Soc. 115, No.2, 313-317 (1992). ISSN 0002-9939; ISSN 1088-6826/e

Let $\{\varphi\sb n\}$ be a positive sequence. The series $\sum a\sb n$ is said to be summable $\vert\overline{N},p\sb n,\varphi\sb n\vert\sb k$, $k\geq 1$, if $\sum\sb{n=1}\sp \infty\varphi\sb n\sp{k-1}\vert T\sb n- T\sb{n-1}\vert\sp k<\infty$, where $T\sb n:=P\sb n\sp{-1}\sum\sb{k=0}\sp n p\sb k s\sb k$. The author obtains sufficient conditions for the series $\sum a\sb n\varepsilon\sb n$ to be summable $\vert\overline{N},p\sb n,\varphi\sb n\vert\sb k$.
MSC 2000:
*40D15 Convergence factors and summability factors
40G99 Special methods of summability
40F05 Special cases of summability

Keywords: summability factors; weighted mean method

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