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Logarithmic convexity of extended mean values. (English) Zbl 0993.26012

The author investigates the logarithmic convexity of the extended mean value introduced by K. B. Stolarsky [Math. Mag. 48, 87-92 (1975; Zbl 0302.26003)]. For the arithmetic, logarithmic and identric means of two variables, the inequality \(A+ L< 2I\) is proved. Two open problems are proposed.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
26E60 Means
26B25 Convexity of real functions of several variables, generalizations

Citations:

Zbl 0302.26003
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References:

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