A subadditive property of the error function

Alzer, Horst; Kwong, Man

doi:10.1090/S0002-9939-2014-11996-4

A subadditive property of the error function
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Proc. Amer. Math. Soc. 142 (2014), 2697-2704 Request permission

Abstract:

We prove the following subadditive property of the error function: \[ \mbox {erf} (x)=\frac {2}{\sqrt {\pi }}\int _0^x e^{-t^2}dt \quad {(x\in \mathbf {R})}. \] Let $a$ and $b$ be real numbers. The inequality \[ \mbox {erf} \bigl ((x+y)^a\bigr )^b< \mbox {erf} (x^a)^b + \mbox {erf} (y^a)^b \] holds for all positive real numbers $x$ and $y$ if and only if $ab\leq 1$.

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