# Redundancy Conditions for the Functional Equation $f(x+h(x))=f(x)+f(h(x))$

### Gian Luigi Forti

Università di Milano, Italy

## Abstract

Consider the functional equation $f(x+h(x))=f(x)+f(h(x))$, where $h:R→R$ is a given continuous function, $h(0)=0$. It is proved if the set of all zeros of $h$ and of all points where $h(x)=−x$ is not "too much dense", then the continuous and at $x=0$ differentiable solution $f:R→R$ of the functional equation under consideration is $f(x)=xf’(0)$ for all real $x$.

## Cite this article

Gian Luigi Forti, Redundancy Conditions for the Functional Equation $f(x+h(x))=f(x)+f(h(x))$. Z. Anal. Anwend. 3 (1984), no. 6, pp. 549–554

DOI 10.4171/ZAA/129