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A Kuczma-type functional inequality for error and complementary error functions

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Abstract

We prove that the functional inequality

$$x + {\rm erf} \bigl(y + {\rm erf}_c(x)\bigr) < y + {\rm erf} \bigl(x + {\rm erf}_c(y)\bigr)$$

is valid for all real numbers x and y with 0 ≤ x < y. Here, erf and erf c denote the error and the complementary error functions, respectively.

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  1. Morsbacher Str. 10, 51545, Waldbröl, Germany

    Horst Alzer

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  1. Horst Alzer
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Alzer, H. A Kuczma-type functional inequality for error and complementary error functions. Aequat. Math. 89, 927–935 (2015). https://doi.org/10.1007/s00010-014-0289-z

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  • DOI: https://doi.org/10.1007/s00010-014-0289-z

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