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A generalized mixed type of quartic-cubic-quadratic-additive functional equations. (English) Zbl 1247.39023

Let $k\notin \left\{0,±1\right\}$ be a fixed integer. The authors give the general solution of the functional equation

$f\left(x+ky\right)+f\left(x-ky\right)=g\left(x+y\right)+g\left(x-y\right)+h\left(x\right)+h\left(y\right)·$

In fact, the main result of the paper is a straightforward consequence of a particular case of L. Székelyhidi’s result [Convolution type functional equations on topological abelian groups, Singapore etc.: World Scientific (1991; Zbl 0748.39003)].

##### MSC:
 39B22 Functional equations for real functions 39B52 Functional equations for functions with more general domains and/or ranges
##### References:
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