A generalized mixed type of quartic-cubic-quadratic-additive functional equations (Q765396)

Let \(k\not\in\{0,\pm 1\}\) be a fixed integer. The authors give the general solution of the functional equation \[ f(x+ky)+f(x-ky)=g(x+y)+g(x-y)+h(x)+h(y). \] In fact, the main result of the paper is a straightforward consequence of a particular case of \textit{L. Székelyhidi}'s result [Convolution type functional equations on topological abelian groups, Singapore etc.: World Scientific (1991; Zbl 0748.39003)].