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arXiv · 1904.12612

On the equality of Bajraktarevi\'c means to quasi-arithmetic means

Zsolt Páles·Amr Zakaria
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Abstract

This paper offers a solution of the functional equation $$ \big(tf(x)+(1-t)f(y)\big)\varphi(tx+(1-t)y)=tf(x)\varphi(x)+(1-t)f(y)\varphi(y) \qquad(x,y\in I), $$ where $t\in\,]0,1[\,$ is a fixed number, $\varphi:I\to\mathbb{R}$ is strictly monotone, and $f:I\to\mathbb{R}$ is an arbitrary unknown function. As an immediate application, we shed new light on the equality problem of Bajraktarevi\'c means with quasi-arithmetic means.

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Zsolt Páles, Amr Zakaria. 2019-04-29. On the equality of Bajraktarevi\'c means to quasi-arithmetic means. https://doi.org/10.1007/s00025-019-1141-5

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