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Volume 5, Issue 3, 1 June 2021, Pages 331-351
Abstract. We use an implementation of the generic approach to solve (generalized) stochastic feasibility problems. These are the problems of finding almost common fixed points of measurable (with respect to a probability measure) families of mappings. Such an implementation for a bounded set K has already been presented by Gabour, Reich and Zaslavski in 2001. Our strong convergence results provide iterative methods (in the case where the set K is not necessarily bounded) for finding an almost common fixed point of a generic measurable family of mappings. Some of our results involve the case where a subset of the almost common fixed point set is a nonexpansive retract of K. Our results are applicable to both the consistent case (that is, the case where the aforesaid almost common fixed points exist) and the inconsistent case (that is, the case where there are no common fixed points at all).
How to Cite this Article:
Kay Barshad, Simeon Reich, Alexander J. Zaslavski, Generic convergence of methods for solving stochastic feasibility problems, J. Nonlinear Var. Anal. 5 (2021), 331-351.