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Inclusion Relations for General Riesz Typical Means

Published online by Cambridge University Press:  20 November 2018

A. Jakimovski  and
J. Tzimbalario
A. Jakimovski
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
J. Tzimbalario
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
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Let α be a non-negative real number, λ≡{λ,n}(n≥0) a strictly increasing unbounded sequence with λ0≥0 and let be an arbitrary series with partial sums s≡{sn}. Write

where s(t)=sn for λn<t≤λn+1, s(t)=0 for 0≤t≤λ0. The series ∑ an or the sequence of partial sums s={sn} is summable to ṡ by the Riesz method (R, λ, α) if

as ω→∞.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 51 - 61
Copyright
Copyright © Canadian Mathematical Society 1974

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