A Sharp Double Inequality between Harmonic and Identric Means

Yu-Ming Chu, Miao-Kun Wang and Zi-Kui Wang

Abstract and Applied Analysis, 2011, vol. 2011, 1-7

Abstract:

We find the greatest value ð ‘ and the least value ð ‘ž in ( 0 , 1 / 2 ) such that the double inequality ð » ( ð ‘ ð ‘Ž + ( 1 − ð ‘ ) ð ‘ , ð ‘ ð ‘ + ( 1 − ð ‘ ) ð ‘Ž ) < ð ¼ ( ð ‘Ž , ð ‘ ) < ð » ( ð ‘ž ð ‘Ž + ( 1 − ð ‘ž ) ð ‘ , ð ‘ž ð ‘ + ( 1 − ð ‘ž ) ð ‘Ž ) holds for all ð ‘Ž , ð ‘ > 0 with ð ‘Ž â‰ ð ‘ . Here, ð » ( ð ‘Ž , ð ‘ ) , and ð ¼ ( ð ‘Ž , ð ‘ ) denote the harmonic and identric 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:657935

DOI: 10.1155/2011/657935

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