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Logarithmic convexity of the one-parameter mean values. (English) Zbl 1132.26324
Summary: The logarithmic convexity of the one-parameter mean values $$J(r)$$ and the monotonicity of the product $$J(r)J(-r)$$ with $$r\in\mathbb{R}$$ are presented. Some more general results are established.

##### MSC:
 26A48 Monotonic functions, generalizations 26A51 Convexity of real functions in one variable, generalizations 26B25 Convexity of real functions of several variables, generalizations 26D07 Inequalities involving other types of functions
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