Superstability of p-Radical Functional Equations Related to Wilson-Kannappan-Kim Functional Equations

초록

In the present paper, we introduce and solve the following p-radical functional equations related to trigonometric functional equations f (p root x(p) + y(p)) + f (p root x(p) - y(p) = 2f(x)f(y), f (p root x(p) + y(p)) + f (p root x(p) - y(p)) = 2f(x)g(y), and f (p root x(p) + y(p)) + f (p root x(p) - y(p) = 2g(x)f(y) for all x, y. R where f, g are functions from R into C and p is an odd positive integer. Furthermore, we investigate the superstability of those functional equations. As consequence, we extend our results to Banach algebras.

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