Convergence of iterative methods for solving random operator equations (Q2876427)

In the paper under review, probabilistic quasi-nonexpansive (and strict quasi-nonexpansive) mappings with Nishiura ``distances'' are considered. For such mappings, some interesting properties are presented. In particular, under some additional conditions on such a quasi-nonexpansive mapping \(T\) (continuity on a closed subset of a domain, existence of a convergent subsequence), it is proved that the sequence of successive approximations of \(T\), starting from some point of the domain, is convergent to a unique fixed point of \(T\). Moreover, strict quasi-nonexpansive mappings with probabilistic metric are considered.