We solve two Pexiderized extensions of the quadratic functional equation on monoids. The equation is extended by replacing the group inversion in the classical quadratic equation with an involution, which may be either homomorphic or anti-homomorphic. Also two extensions of the Drygas functional equation are solved in the same setting. In all results it is assumed that at least one unknown function is central.

中文翻译：

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关于mono半群的一些广义二次函数方程

我们解决了关于mono半群的二次函数方程的两个Pexiderized扩展。通过用对合替换经典二次方程组中的群求逆来扩展方程，该对合可以是同态的或反同态的。在相同的设置下，还解决了Drygas功能方程式的两个扩展问题。在所有结果中，假定至少一个未知函数是中心。