Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means

Yu-Ming Chu and Bo-Yong Long

Abstract and Applied Analysis, 2010, vol. 2010, 1-13

Abstract:

We answer the question: for α , β , γ ∈ ( 0,1 ) with α + β + γ = 1 , what are the greatest value p and the least value q , such that the double inequality L p ( a , b ) < A α ( a , b ) G β ( a , b ) H γ ( a , b ) < L q ( a , b ) holds for all a , b > 0 with a ≠ b ? Here L p ( a , b ) , A ( a , b ) , G ( a , b ) , and H ( a , b ) denote the generalized logarithmic, arithmetic, geometric, and harmonic means of two positive numbers a and b , respectively.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:303286

DOI: 10.1155/2010/303286

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