The Inequalities $G\leq L\leq I\leq A$ in $n$ Variables

Volume 4, Issue 2, 2003

Article 39

THE INEQUALITIES IN $n$ VARIABLES

DEPARTMENT OF MATHEMATICS,
HUNAN INSTITUTE OF SCIENCE AND TECHNOLOGY,
YUEYANG CITY, HUNAN 414006,
CHINA.
E-Mail: xzgzzh@163.com

ZIXING EDUCATIONAL RESEARCH SECTION,
CHENZHOU CITY,
HUNAN 423400, CHINA.
E-Mail: zxzh1234@163.com

Received 21 October, 2002; Accepted 28 March, 2003.
Communicated by: F. Qi

ABSTRACT. In the short note, the inequalities $G\le L\le I\le A$ for the geometric, logarithmic, identric, and arithmetic means in

variables are proved.

Key words:
Inequality, Arithmetic mean, Geometric mean, Logarithmic mean, Identric mean, $n$ variables, Van der Monde determinant.

2000 Mathematics Subject Classification:
26D15.

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