Let R be a non-expansive operator from R^2 into R^2 and x* be a fixed point of this operator (we assume that there is one).
Take x in R^2, we represent here in red the possibles points for R(x).
Let α in ]0,1[. An operator T is said to be α-averaged if T = (1- α) Id + α R for some non-expansive (NE) operator R.
We will build in blue the possibles points for x'=T(x).
First, please set α. It shall be strictly between 0 and 1 but the limits values are allowed in this illustration.
The default value 0.5 corresponds to a firmly non-expansive operator.
If you wish, you can make R contracting by tuning the contraction factor β.
The default value 1 correspond to a non-expansive operator.
Finally, you may play the illustration.