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Absolute Tauberian constants for Cesàro means


Author: Soraya Sherif
Journal: Trans. Amer. Math. Soc. 168 (1972), 233-241
MSC: Primary 40D10; Secondary 40G05
DOI: https://doi.org/10.1090/S0002-9947-1972-0294945-0
MathSciNet review: 0294945
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Abstract: This paper is concerned with introducing two inequalities of the form $ \sum\nolimits_{n = 0}^\infty {\vert{\tau _n}} - {a_n}\vert \leqq KA$ and $ \sum\nolimits_{n = 0}^\infty {\vert{\tau _n}} - {a_n}\vert \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 {\vert\Delta (n{a_n}} )\vert < \infty ,B = \s... ...ty {\vert\Delta ((1/n)\sum\nolimits_{v = 1}^{n - 1} {v{a_v}} } )\vert < \infty $ and $ \Delta {u_k} = {u_k} - {u_{k + 1}}$. The constants $ K,K'$ will be determined.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0294945-0
Article copyright: © Copyright 1972 American Mathematical Society

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