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

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Ukrainian Mathematical Journal Aims and scope

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 functions f, g, h, and0020\( \tilde{h} \). The method used for solving these functional equations is elementary but it exploits an important result due to Hosszú. The solution of this functional equation can also be obtained in groups of certain type by using two important results due to Székelyhidi.

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Authors and Affiliations

  1. School of Science, Beijing Institute of Technology, Beijing, China

    T. Z. Xu

  2. National and Kapodistrian University of Athens, Athens, Greece

    J. M. Rassias

  3. University of Electronic Science and Technology of China, Chengdu, China

    W. X. Xu

Authors
  1. T. Z. Xu
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  2. J. M. Rassias
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  3. W. X. Xu
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 399–415, March, 2011.

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Xu, T.Z., Rassias, J.M. & Xu, W.X. A generalized mixed type of quartic–cubic–quadratic–additive functional equations. Ukr Math J 63, 461–479 (2011). https://doi.org/10.1007/s11253-011-0515-y

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  • DOI: https://doi.org/10.1007/s11253-011-0515-y

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