Random products of contractions in metric and Banach Spaces

Suppose (X, d) is a metric space and {T₀,…, T_N} is a family of quasinonexpansive self-mappings on X. We give conditions sufficient to guarantee that every possible iteration of mappings drawn from {T₀,…, T_N} converges. As a consequence, if C₀,…, C_N are closed convex subsets of a Hilbert space with nonempty intersection, one of which is compact, and the proximity mappings are iterated in any order (provided only that each is used infinitely often), then the resulting sequence converges strongly to a point of the common intersection.