Abstract In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation: ϕ ( s t − u v ) + ϕ ( s v + t u ) = [ ϕ ( s ) + ϕ ( u ) ] [ ϕ ( t ) + ϕ ( v ) ] \phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)] by using the direct method and the fixed point method.

中文翻译：

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关于具有二次乘性性质的函数方程

摘要 在本文中，我们获得了以下二次乘法函数方程的通解并证明了 Hyers-Ulam 稳定性： ϕ ( st − uv ) + ϕ ( sv + tu ) = [ ϕ ( s ) + ϕ ( u ) ] [ ϕ ( t ) + ϕ ( v ) ] \phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t )+\phi (v)] 使用直接法和定点法。