Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form \begin{equation*} C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left( x\right) \cdot g\left( y\right) \right) \text{,} \end{equation*} where $f,g$ are bijections of $I$ are considered. Their connections with generalized weighted quasi-geometric means is presented. It is shown that invariance question within the class of this operations leads to means of iterative type and to a problem on a composite functional equation. An application of the invariance identity to determine effectively the limit of the sequence of iterates of some generalized quasi-geometric mean-type mapping, and the form of all continuous functions which are invariant with respect to this mapping are given. The equality of two considered operations is also discussed.

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与加权准几何均值相关的一类操作的不变性

令 $I\subset (0,\infty )$ 是一个关于乘法闭合的区间。$C_{f,g}\colon I^{2}\rightarrow I$ 形式为 \begin{equation*} C_{f,g}\left( x,y\right) =\left( f\ circ g\right) ^{-1}\left( f\left( x\right) \cdot g\left( y\right) \right) \text{,} \end{equation*} where $f,g $ 是 $I$ 的双射被考虑。介绍了它们与广义加权准几何平均值的联系。结果表明，该运算类中的不变性问题导致迭代类型的手段和复合函数方程上的问题。给出了应用不变恒等式有效地确定一些广义准几何平均类型映射的迭代序列的极限，以及所有关于该映射不变的连续函数的形式。