Abstract and Applied Analysis

Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means

Yu-Ming Chu and Bo-Yong Long

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 303286, 13 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620708

Digital Object Identifier
doi:10.1155/2010/303286

Mathematical Reviews number (MathSciNet)
MR2607125

Zentralblatt MATH identifier
1185.26064

Citation

Chu, Yu-Ming; Long, Bo-Yong. Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means. Abstr. Appl. Anal. 2010 (2010), Article ID 303286, 13 pages. doi:10.1155/2010/303286. https://projecteuclid.org/euclid.aaa/1288620708


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