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- W2091161298 abstract "The series $Sigma _{n = 1}^infty {a_n}$ is said to be summable $(L)$ to $s$ if ${(log (1 - x))^{ - 1}}Sigma _{n = 1}^infty {s_n}{x^{n + 1}}/n$, where ${s_n} = Sigma _{v = 1}^n{a_v}$, converges for $0 leq x < 1$ and tends to $s$ when $x to 1 -$. The aim of this paper is to discuss the relation between summability $(L)$ and Riesz summability $(R,log n,kappa )$. It is proved that $(R,log n,kappa ) subseteq (L)$ holds for $0 leq kappa leq 1$ and is false for $kappa > 1$. It is also proved that if $Sigma _{n = 1}^infty {a_n} = s(L)$ and bounded $(R,log n,kappa )$ for $kappa geq 0$ then $Sigma _{n = 1}^infty {a_n} = s(R,log n,kappa + delta )$ for every $delta > 0$." @default.
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- W2091161298 date "1974-03-01" @default.
- W2091161298 modified "2023-10-14" @default.
- W2091161298 title "The Riesz summability of logarithmic type" @default.
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- W2091161298 doi "https://doi.org/10.1090/s0002-9939-1974-0348326-9" @default.
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