Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means

Yu-Ming Chu, Shan-Shan Wang and Cheng Zong

Abstract and Applied Analysis, 2011, vol. 2011, 1-9

Abstract:

We find the least value 𠜆 ∈ ( 0 , 1 ) and the greatest value ð ‘ = ð ‘ ( ð ›¼ ) such that ð ›¼ ð » ( ð ‘Ž , ð ‘ ) + ( 1 − ð ›¼ ) ð ¿ ( ð ‘Ž , ð ‘ ) > ð ‘€ ð ‘ ( ð ‘Ž , ð ‘ ) for ð ›¼ ∈ [ 𠜆 , 1 ) and all ð ‘Ž , ð ‘ > 0 with ð ‘Ž â‰ ð ‘ , where ð » ( ð ‘Ž , ð ‘ ) , ð ¿ ( ð ‘Ž , ð ‘ ) , and ð ‘€ ð ‘ ( ð ‘Ž , ð ‘ ) are the harmonic, logarithmic, and ð ‘ -th power means of two positive numbers ð ‘Ž and ð ‘ , respectively.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:520648

DOI: 10.1155/2011/520648

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