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Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-22
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We prove that αH(a,b)+(1−α)L(a,b)>M(1−4α)/3(a,b) for α∈(0,1) and all a,b>0 with a≠b if and only if α∈[1/4,1) and αH(a,b)+(1−α)L(a,b) Here, H(a,b)=2ab/(a+b), L(a,b)=(a−b)/(log a−log b), and Mp(a,b)=((ap+bp)/2)1/p (p≠0) and M0(a,b)=ab are the harmonic, logarithmic, and pth power means of a and b, respectively.
American Psychological Association (APA)
Qian, Wei-Mao& Shen, Zhong-Hua. 2012. Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-1028890
Modern Language Association (MLA)
Qian, Wei-Mao& Shen, Zhong-Hua. Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means. Journal of Applied Mathematics No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-1028890
American Medical Association (AMA)
Qian, Wei-Mao& Shen, Zhong-Hua. Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-1028890
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028890