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    A generalized mixed type of quartic–cubic–quadratic–additive functional equations

    We determine the general solution of the functional equation f(x + ky) + f(x-ky) = g(x + y) + g(x-y) + h(x) + h(y) for fixed integers with k ≠ 0; ±1 without assuming any regularity conditions for the unknown func...

    T. Z. Xu, J. M. Rassias, W. X. Xu in Ukrainian Mathematical Journal (2011)