12- https://doi.org/10.1007/s10114-008-6621-6
On the stability of the generalized sine functional equations
- Nov 17, 2008
- Acta Mathematica Sinica, English Series
- Gwang Hui Kim
Abstract
The aim of this paper is to study the stability problem of the generalized sine functional equations as follows: $$ \begin{array}{*{20}c} {g(x)f(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 ,} \\ {f(x)g(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 ,} \\ {g(x)g(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 .} \\ \end{array} $$ .
