# IJPAM: Volume 72, No. 1 (2011)

THE OPTIMAL GENERALIZED
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

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