  In his recent research M. K. Tam (2018) considered a framework for the
analysis of iterative algorithms which can be described in terms of a
structured set-valued operator. At each point in the ambient space, the value
of the operator can be expressed as a finite union of values of single-valued
paracontracting operators. He showed that the associated fixed point iteration
is locally convergent around strong fixed points. This result generalizes a
theorem due to Bauschke and Noll (2014). In the present paper we generalize the
result of Tam and show the global convergence of his algorithm for an arbitrary
starting point. An analogous result is also proved for the Krasnosel'ski-Mann
iterations.
