Starting from the inequality $$\begin{aligned} |f(x+y)-f(x)-f(y)+g(x+y)-g(x)g(y)|\leqslant \varepsilon , \quad x,y\in S, \end{aligned}$$ | f ( x + y ) - f ( x ) - f ( y ) + g ( x + y ) - g ( x ) g ( y ) | ⩽ ε , x , y ∈ S , where f is a complex valued function defined on a monoid S , we deal with two problems: the stability problem and the problem of alienation of the approximate additivity condition from the condition of approximate exponentiality.

中文翻译：

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异化与稳定性问题

从不等式 $$\begin{aligned} |f(x+y)-f(x)-f(y)+g(x+y)-g(x)g(y)|\leqslant \varepsilon 开始， \quad x,y\in S, \end{aligned}$$ | f ( x + y ) - f ( x ) - f ( y ) + g ( x + y ) - g ( x ) g ( y ) | ⩽ ε , x , y ∈ S ，其中 f 是定义在幺半群 S 上的复值函数，我们处理两个问题：稳定性问题和近似可加性条件与近似指数条件的异化问题。