Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means

Bo-Yong Long, Yu‐Ming Chu

Type: Article

Publication Date: 2010-01-01

Citations: 35

DOI: https://doi.org/10.1155/2010/806825

Abstract

For , the generalized logarithmic mean , arithmetic mean , and geometric mean of two positive numbers and are defined by , for , , for , , and , , for , and , , for , and , , and , respectively. In this paper, we find the greatest value (or least value , resp.) such that the inequality (or , resp.) holds for (or , resp.) and all with .

Locations

DOAJ (DOAJ: Directory of Open Access Journals) - View
Journal of Inequalities and Applications - View - PDF

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Works Cited by This (18)

Action	Title	Year	Authors
+ PDF Chat	Monotonicity result for generalized logarithmic means	2007	Xin Li Ch.-P. Chen Feng Qi
+	On the identric and logarithmic means	1990	József Sándor
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+	Inequalities for Means in Two Variables	2003	Horst Alzer Song-Liang Qiu
+	Extended mean values II	1983	E. B. Leach Marlow Sholander
+	A note on some inequalities for means	1991	J. S�ndor
+	The monotonicity of the ratio between generalized logarithmic means	2008	Chao-Ping Chen
+	The Power Mean and the Logarithmic Mean	1974	Tung‐Po Lin