# Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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## Absolute Tauberian constants for Cesàro meansHTML articles powered by AMS MathViewer

by Soraya Sherif
Trans. Amer. Math. Soc. 168 (1972), 233-241 Request permission

## Abstract:

This paper is concerned with introducing two inequalities of the form $\sum \nolimits _{n = 0}^\infty {|{\tau _n}} - {a_n}| \leqq KA$ and $\sum \nolimits _{n = 0}^\infty {|{\tau _n}} - {a_n}| \leqq K’B$, where ${\tau _n} = C_n^{(k)} - C_{n - 1}^{(k)},C_n^{(k)}$ denote the Cesàro transform of order $k,K$ and $K’$ are absolute Tauberian constants, $A = \sum \nolimits _{n = 0}^\infty {|\Delta (n{a_n}} )| < \infty ,B = \sum \nolimits _{n = 0}^\infty {|\Delta ((1/n)\sum \nolimits _{v = 1}^{n - 1} {v{a_v}} } )| < \infty$ and $\Delta {u_k} = {u_k} - {u_{k + 1}}$. The constants $K,K’$ will be determined.
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