Iterative methods of solving stochastic convex feasibility problems and applications

The stochastic convex feasibility problem (SCFP) is the problem of finding almost common points of measurable families of closed convex subsets in ref lexive and separable Banach spaces. In this paper we prove convergence crit eria for two iterative algorithms devised to solve SCFPs. To do that, we fi rst analyze the concepts of Bregman projection and Bregman function with em phasis on the properties of their local moduli of convexity. The areas of a pplicability of the algorithms we present include optimization problems, li near operator equations, inverse problems, etc., which can be represented a s SCFPs and solved as such. Examples showing how these algorithms can be im plemented are also given.