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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of strong Rieszian summability


Author: L. I. Holder
Journal: Proc. Amer. Math. Soc. 42 (1974), 452-460
MSC: Primary 40F05
MathSciNet review: 0348328
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Abstract: Strong summability, $ [\alpha ,\beta ;p]$, for the Bosanquet-Linfoot $ (\alpha ,\beta )$ summability method is defined so that $ [\alpha ,0;p]$ is identical to strong Rieszian summability, $ [R;\alpha ,p]$. The main result proved in this paper shows consistency in the sense that $ [\alpha ,\beta ;p]$ summability implies $ [\alpha ',\beta ';q]$ summability, for $ \alpha ' > \alpha$ or $ \alpha ' = \alpha ,\beta ' > \beta $; and $ 1 \leqq q \leqq p$. Also, a necessary condition for $ [\alpha ,\beta ;p]$ summability and relationships between strong and absolute $ (\alpha ,\beta )$ summability are given.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0348328-2
Keywords: Bosanquet-Linfoot summability, Rieszian summability, strong summability, consistency, absolute summability
Article copyright: © Copyright 1974 American Mathematical Society