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A new proof of the monotonicity property of power means. (English) Zbl 1051.26023

Summary: If \(M_r\) is the weighted power mean of the numbers \(x_j\in[a,b]\) then \(Q_r(a,b,x)= (a^r+b^r-M_r^r)^{1/r}\) is increasing in \(r\). A new proof of this fact is given.

MSC:

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