The function (b^x-a^x)/x: Logarithmic convexity and applications to extended mean values
classification
🧮 math.CA
keywords
convexityextendedmeanvaluesfunctionlogarithmicapplicationsbasing
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In the present paper, we first prove the logarithmic convexity of the elementary function $\frac{b^x-a^x}x$, where $x\ne0$ 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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