A lower bound for ratio of power means

Feng Qi, Bai-Ni Guo and Lokenath Debnath

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-5

Abstract:

Let n and m be natural numbers. Suppose that { a i } i = 1 n + m is an increasing, logarithmically convex, and positive sequence. Denote the power mean P n ( r ) for any given positive real number r by P n ( r ) = ( ( 1 / n ) ∑ i = 1 n a i r ) 1 / r . Then P n ( r ) / P n + m ( r ) ≥ a n / a n + m . The lower bound is the best possible.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:705832

DOI: 10.1155/S0161171204208158

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