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Functional means and harmonic functional means
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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- Research Article
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- Copyright © Australian Mathematical Society 1998
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