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- W2002828081 abstract "Bosanquet [2] showed that a necessary and sufficient condition for $Sigma _{k = 1}^infty {x_k}{y_k}$ to be Cesà ro summable of order $n$ ($n$ is a nonnegative integer) whenever $sigma _k^n(y) = o(k)$ where $sigma _k^n(y)$ is the $k$ th Cesà ro mean of $y$ of order $n$ is that $Sigma _{k = 1}^infty {k^{n + 1}}|{Delta ^{n + 1}}{x_k}| < infty$ and ${lim _{k to 0}}k{x_k} = 0$. The main result of this paper is to show that a necessary and sufficient condition for $Sigma _{k = 1}^infty {x_k}{y_k}$ to be Cesà ro summable of order $n$ ($n$ is a nonnegative integer) whenever $Sigma _{k = 1}^infty {k^{n + 1}}|{Delta ^{n + 1}}{x_k}| < infty$ and ${lim _{k to infty }}k{x_k} = 0$ is that $sigma _k^n(y) = o(k)$." @default.
- W2002828081 created "2016-06-24" @default.
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- W2002828081 date "1976-01-01" @default.
- W2002828081 modified "2023-09-26" @default.
- W2002828081 title "Some remarks on summability factors" @default.
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- W2002828081 doi "https://doi.org/10.1090/s0002-9939-1976-0412664-3" @default.
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