Improved regularity for a composite functional equation stemming from the theory of means
Classical Analysis and ODEs
2026-02-18 v1
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 . Improving previous results we assume differentiability on each involved function, eliminate a former condition on and , 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.
Keywords
Cite
@article{arxiv.2602.15541,
title = {Improved regularity for a composite functional equation stemming from the theory of means},
author = {Tibor Kiss and Péter Tóth},
journal= {arXiv preprint arXiv:2602.15541},
year = {2026}
}