On a Result of Levin and SteÄ kin

Peng Gao

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-15

Abstract:

The following inequality for 0 < ð ‘ < 1 and ð ‘Ž ð ‘› ≥ 0 originates from a study of Hardy, Littlewood, and Pólya: ∑ ∞ ð ‘› = 1 ∑ ( ( 1 / ð ‘› ) ∞ 𠑘 = ð ‘› ð ‘Ž 𠑘 ) ð ‘ â‰¥ ð ‘ ð ‘ âˆ‘ ∞ ð ‘› = 1 ð ‘Ž ð ‘ ð ‘› . Levin and SteÄ kin proved the previous inequality with the best constant ð ‘ ð ‘ = ( ð ‘ / ( 1 − ð ‘ ) ) ð ‘ for 0 < ð ‘ â‰¤ 1 / 3 . In this paper, we extend the result of Levin and SteÄ kin to 0 < ð ‘ â‰¤ 0 . 3 4 6 .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:534391

DOI: 10.1155/2011/534391

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