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Functional means and harmonic functional means

Published online by Cambridge University Press:  17 April 2009

Soon-Yeong Chung
Soon-Yeong Chung
Affiliation:
Department of MathematicsSogang UniversitySeoul 121–742Korea e-mail: [email protected]
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Abstract

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For a continuous function f(t) on (0, ∞) which is strictly monotone and a probability measure μ on [0, 1] we introduce the functional mean and the harmonic functional mean of x > 0 and y > 0 with respect to μ by

which gives a unified approach to various famous means.

Moreover, functional means and harmonic means in n variables are also given and applied to get many interesting properties, such as

where

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 207 - 220
Copyright
Copyright © Australian Mathematical Society 1998

References

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