Stability of a sexvigintic functional equation

초록

In this paper, we estabilish the general solution of sexvigintic functional equation f (x + 13y) - 26f (x + 12y) + 325f (x + 11y) - 2600f (x + 10y) + 14950f (x + 9y) -65780f (x + 8y) + 230230f (x + 7y) - 657800f (x + 6y) + 1562275f (x + 5y) -3124550f (x + 4y) + 5311735f (x + 3y) - 7726160f (x + 2y) + 9657700f (x + y) -10400600f (x) + 9657700f (x - y) - 7726160f (x - 2y) + 5311735f (x - 3y) -3124550f (x - 4y) + 1562275f (x - 5y) - 657800f (x - 6y) + 230230f (x - 7y) -65780f (x - 8y) + 14950f (x - 9y) - 2600f (x - 10y) + 325f (x - 11y) -26f(x - 12y) + f (x - 13y) = 26!f(y) and investigate the Hyers-Ulam stability of this functional equation in Banach spaces using two different methods.

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