AN ALGORITHM BASED ON A SET-VALUED MAPPING IN A METRIC SPACE

Abstract

In our recent paper, we generalized a convergence result of Tam (2018) which was proved for iterates of a
set-valued operator such that its values can be expressed as a finite union of values of single-valued paracontracting
operators. It was shown that this convergence result is true for a general set-valued mapping such that its values
are not necessarily finite unions of values of single-valued operators. The result was obtained for exact iterates of a
mapping acting in a finite-dimensional space. In the present paper we will generalize this result for inexact iterates
of a set-valued mapping acting in a metric spaces.