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arXiv · 2602.15541

Improved regularity for a composite functional equation stemming from the theory of means

Tibor Kiss·Péter Tóth
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Abstract

In this paper we describe the solutions of the functional equation \begin{equation*} F\Big(\frac{x+y}2\Big)+f_1(x)+f_2(y)=G \big(g_1(x)+g_2(y)) \end{equation*} defined on an open subinterval of $ \mathbb{R} $. Improving previous results we assume differentiability on each involved function, eliminate a former condition on $ g'_1 $ and $ g'_2$, moreover we determine a brand new family of solutions. We also present a particular member of this class as an example. In order to achieve this, we strengthen known results about certain auxiliary functional equations as well.

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Tibor Kiss, Péter Tóth. 2026-02-17. Improved regularity for a composite functional equation stemming from the theory of means. https://arxiv.org/abs/2602.15541

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