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

• Published in: Український математичний журнал
• Date: 2011
• Main Authors: Rassias, J.M., Xu, T.Z., Xu, W.X.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/166015
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A generalized mixed type of quartic, cubic, quadratic and additive functional equation / J.M. Rassias, T.Z. Xu, W.X. Xu // Український математичний журнал. — 2011. — Т. 63, № 3. — С. 399–415. — Бібліогр.: 23 назв. — англ.

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 k with k 6= 0, ±1 without assuming any regularity condition on the unknown
 functions f, g, h, h˜. The method used for solving these functional equations is e...