MMN-4320

# Decomposition of functional equations with applications

• Tamás Glavosits, University of Miskolc, Department of Applied Mathematics, H-3515 Miskolc-Egyetemváros, Hungary, matgt@uni-miskolc.hu
• Attila Házy, University of Miskolc, Department of Applied Mathematics, H-3515 Miskolc-Egyetemváros, Hungary, matha@uni-miskolc.hu
• József Túri, University of Miskolc, Department of Applied Mathematics, H-3515 Miskolc-Egyetemváros, Hungary, matturij@uni-miskolc.hu

## Abstract

In this paper the Decomposition Theorem for functional equations is shown. As an application of this Theorem the two times continuously differentiable solution of the functional equation $$G_{1}(x(x+y))+F_{1}(y)=G_{2}(y(x+y))+F_{2}(y)$$ can be given with unknown functions $G_{i}$, $F_{i}:\mathbb{R}_{+}\to \mathbb{R}$ $(i=1,2)$ where the Equation is fulfilled for all $x,y\in \mathbb{R}_{+}$.

Vol. 23 (2022), No. 2, pp. 691-701
DOI: 10.18514/MMN.2022.4320