Minkowski’s inequality for two variable difference means

Losonczi, László; Páles, Zsolt

doi:10.1090/S0002-9939-98-04125-2

Minkowski’s inequality for two variable difference means
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by László Losonczi and Zsolt Páles PDF

Proc. Amer. Math. Soc. 126 (1998), 779-789 Request permission

Abstract:

We study Minkowski’s inequality \[ D_{a b}(x_1+x_2, y_1+y_2)\le D_{a b}(x_1, y_1)+D_{a b}(x_2,y_2) \quad (x_1,x_2, y_1,y_2\in \mathbb R_+) \] and its reverse where $D_{a b}$ is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters $a,b$) for the inequality above (and for its reverse) to hold.

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