IJPAM: Volume 72, No. 1 (2011)

THE OPTIMAL GENERALIZED
HERONIAN MEAN BOUNDS FOR THE IDENTRIC MEAN

Yefang Qiu$^1$, Miaokun Wang$^2$, Yuming Chu$^2$
$^1$Department of Mathematics
Zhejiang Sci-Tech University
Zhejiang, Hangzhou, 310018, P.R. CHINA
$^2$Department of Mathematics
Huzhou Teachers College
Zhejiang, Huzhou, 313000, P.R. CHINA


Abstract. In this paper, we answer the question: What are the greatest value $p$ and the least value $q$, such that the double inequality $H_{p}(a,b)<I(a,b)<H_{q}(a,b)$ holds for all $a, b>0$ with $a\neq b$? Here, $H_{p}(a,b)$ and $I(a,b)$ denote the $p$-th generalized Heronian mean and identric mean of two positive numbers $a$ and $b$, respectively.

Received: April 9, 2010

AMS Subject Classification: 26E60

Key Words and Phrases: generalized Heron mean, identric mean, logarithmic mean, power mean

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 1