The function (bx-ax)/x: Logarithmic convexity and applications to extended mean values
Abstract
In the present paper, we first prove the logarithmic convexity of the elementary function bx-axx, where x0 and b>a>0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.
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