Abstract

In this survey we present several new and recent results concerning the asymptotic behavior of (random) infinite products of generic sequences of nonexpansive as well as uniformly continuous operators on closed convex subsets of a complete hyperbolic space. (Note that all normed linear spaces are hyperbolic.) Such infinite products find application in the solution of feasibility and optimization problems and in many other areas of mathematics. In addition to weak ergodic theorems and the convergence of infinite products to a unique common fixed point and more generally, to a nonexpansive retraction, we also discuss the convergence of Krasnosel’skii-Mann iterations and of contractive and (F)-attracting mappings.

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