On solutions of $f(x)+f(a_1x)+...+f(a_Nx)=0$ and related equations

Abstract

We study some properties of the solutions of the functional equation $$f(x)+f(a_1x)+...+f(a_Nx)=0,$$ which was introduced in the literature by Mora, Cherruault and Ziadi in 1999, for the case $a_k=k+1$, $k=1,2,...,N$ and studied by Mora in 2008 and Mora and Sepulcre in 2009 and 2011.