A generalized mixed type of quartic, cubic, quadratic and additive functional equation

• Date: 2011
• Main Authors: Rassias, J. M., Xu, T. Z., Xu, W. X., Расіас, Дж. М., Ху, Т. З., Ху, В. Х.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2725
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We determine the general solution of the functional equation $f(x + ky) + f(x — ky) = g(x + y) + g(x — y) + h(x) + \tilde{h}(y)$ forfixed integers $k$ with $k \neq 0, \pm 1$ without assuming any regularity condition on the unknown functions $f, g, h, \tilde{h}$. The method used for solving these f...