Abstract We show that for a given initial point the typical, in sense of Baire category, nonexpansive compact valued mapping F has following properties: there is unique sequence successive approximations and this converges to fixed . In case separable Banach spaces we typical residual set points have trajectory.

The paper is an updated survey of our work on the approximation of univariate setvalued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact conv...