  In this note, we consider a framework for the analysis of iterative
algorithms which can described in terms of a structured set-valued operator.
More precisely, at each point in the ambient space, we assume that the value of
operator can be expressed as a finite union of values of single-valued
paracontracting operators. Our main result, which shows that the associated
fixed point iteration is locally convergent around strong fixed points,
generalises a theorem due to Bauschke and Noll (2014).
