Year: 2026
Type: article
Abstract: In this paper we describe the solutions of the functional equation $$\begin{aligned} F\Big (\frac{x+y}{2}\Big )+f_1(x)+f_2(y)= G \big (g_1(x)+g_2(y)) \end{aligned}$$ F ( x + y 2 ) + f 1 ( x ) + f 2 ( y ) = G ( g 1 ( x ) + g 2 ( y ) ) defined on an open subinterval of $$ {\mathbb {R}} $$ R . Improving previous results we assume differentiability on each involved function, eliminate a former condition on $$ g'_1 $$ g 1 ′ and $$ g'_2 \, $$ 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.
Source: Results in Mathematics
Authors: Tibor Kiss, Péter Tóth
Institution: University of Debrecen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G2290027075, G2663030701
OpenAlex ID: W7118939297