Abstract
We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: and, 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.
Highlights
Baker et al in 1 stated the following: if f satisfies the inequality |E1 f − E2 f | ≤ ε, either f is bounded or E1 f E2 f
The superstability of the Wilson equation fxyfx − y 2f x g y, Cf g was investigated by Kannappan and Kim 9
The superstability of the trigonometric functional equation concerned with the sine and the cosine equations f x y − f x − y 2f x f y, T
Summary
Department of Mathematics, Kangnam University, Yongin, Gyeonggi 446-702, South Korea Copyright q 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. 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.
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