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Transactions of the American Mathematical Society

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

 
 

 

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 $\sum \nolimits _{n = 0}^\infty {|{\tau _n}} - {a_n}| \leqq KA$ 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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Article copyright: © Copyright 1972 American Mathematical Society