IJPAM: Volume 72, No. 1 (2011)
THE OPTIMAL GENERALIZED
HERONIAN MEAN BOUNDS FOR THE IDENTRIC MEAN
HERONIAN MEAN BOUNDS FOR THE IDENTRIC MEAN
Yefang Qiu
, Miaokun Wang
, Yuming Chu
Department of Mathematics
Zhejiang Sci-Tech University
Zhejiang, Hangzhou, 310018, P.R. CHINA
Department of Mathematics
Huzhou Teachers College
Zhejiang, Huzhou, 313000, P.R. CHINA




Zhejiang Sci-Tech University
Zhejiang, Hangzhou, 310018, P.R. CHINA

Huzhou Teachers College
Zhejiang, Huzhou, 313000, P.R. CHINA
Abstract. In this paper, we answer the question: What are the greatest value and the least value
, such that the double inequality
holds for all
with
? Here,
and
denote the
-th generalized Heronian mean and identric mean of two positive numbers
and
, 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