  The invariance identity involving three operations $D_{f,g}:X\times
X\rightarrow X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left(
f\circ g\right) ^{-1}\left( f\left( x\right) \oplus g\left( y\right) \right)
\text{,} \end{equation*} is proposed. The connections of these operations with
means is investigated. The question when the invariance equality admits three
means leads to a composite functional equation. Problem to determine its
continuous solutions is posed.
