Volume 3,  Issue 5, 2002

Article 71

A MONOTONICITY PROPERTY OF RATIOS OF SYMMETRIC HOMOGENEOUS MEANS

PETER A. HÄSTÖ

DEPARTMENT OF MATHEMATICS, 
P.O. BOX 4, 
00014 UNIVERSITY OF HELSINKI.
E-Mail: peter.hasto@helsinki.fi

Received 23 February, 2002; Accepted 24 September, 2002.
Communicated by: F. Qi

ABSTRACT.   We study a certain monotonicity property of ratios of means, which we call a strong inequality. These strong inequalities were recently shown to be related to the so-called relative metric. We also use the strong inequalities to derive new ordinary inequalities. The means studied are the extended mean value of Stolarsky, Gini's mean and Seiffert's mean.
Key words:
Monotonicity, Strong inequalities, Extended mean values, Gini's mean, Seiffert's mean, Relative metrics.

2000 Mathematics Subject Classification:
Primary: 26E60; Secondary: 26D15, 26D05.

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