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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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