Filomat 2011 Volume 25, Issue 4, Pages: 63-73
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The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values

Guo Bai-Ni, Feng Qi

In the paper, we first prove the logarithmic convexity of the elementary function bx−ax/x, where x ≠ 0 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.

Keywords: Schur-convexity, Extended mean values, Lazarević’s inequality

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