Copyright © 2010 Gwang Hui Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y)±g(x−y)=λf(x)g(y) andf(x+y)±g(x−y)=λg(x)f(y), which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.