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Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-03
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We find the least values p, q, and s in (0, 1/2) such that the inequalities H(pa+(1 − p)b, pb+(1 − p)a)>AG(a,b), G(qa+(1−q)b, qb+(1−q)a)>AG(a,b), and L(sa+(1−s)b,sb+(1−s)a)> AG(a,b) hold for all a,b>0 with a≠b, respectively.
Here AG(a,b), H(a,b), G(a,b), and L(a,b) denote the arithmetic-geometric, harmonic, geometric, and logarithmic means of two positive numbers a and b, respectively.
American Psychological Association (APA)
Chu, Yu-Ming& Wang, Miao-Kun. 2011. Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-485625
Modern Language Association (MLA)
Chu, Yu-Ming& Wang, Miao-Kun. Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means. Journal of Applied Mathematics No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-485625
American Medical Association (AMA)
Chu, Yu-Ming& Wang, Miao-Kun. Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-485625
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-485625