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

Let k{0,±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 L. Székelyhidi’s result [Convolution type functional equations on topological abelian groups, Singapore etc.: World Scientific (1991; Zbl 0748.39003)].

MSC:
39B22Functional equations for real functions
39B52Functional equations for functions with more general domains and/or ranges
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