Abstract:

Let X be a vector space and Y be a Banach space over the real field, R. A mapping f:X2→Y from X2 into Y is called a mixed quintic functional equation of two variables if it satisfies that f(x1+x2, 2y1+y2)+f(x1+x2,2y1-y2)+f(x1-x2, 2y1+y2)+f(x1-x2, 2y1-y2)=4f(x1,y1+y2)+4f(x2, y1+y2)+4f(x1,y1-y2)+4f(x2, y1-y2)+24f(x1, y1)+24f(x2, y1) for all x1, x2, y1, y2∈X. The general solution of the mixed quintic functional equation of two variables is obtained and the Hyers-Ulam-Rassias stability for it is proved.

Key words: Hyers-Ulam-Rassias stability; the mixed quintic functional equation of two variables; Banach space