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Authors: KAY BARSHAD, SIMEON REICH, ALEXANDER J. ZASLAVSKI.
DOI: 10.24193/subbmath.2022.1.01
Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 11-19
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The notion of porosity is well known in Optimization and Nonlinear Analysis. Its importance is brought out by the fact that the complement of a $sigma$-porous subset of a complete pseudo-metric space is a residual set, while the existence of the latter is essential in many problems which apply the generic approach. Thus, under certain circumstances, some refinements of known results can be achieved by looking for porous sets. In 2001, Gabour, Reich and Zaslavski developed certain generic methods for solving stochastic feasibility problems. This topic was further investigated in 2021 by Barshad, Reich and Zaslavski, who provided more general results in the case of unbounded sets. In the present paper we introduce and examine new generic methods that deal with the aforesaid problems, in which, in contrast with previous studies, we consider sigma-porous sets instead of meager ones.
Keywords: Baire category, Banach space, common _xed point problem, generic convergence, porous set, residual set, stochastic feasibility problem.
Mathematics Subject Classification (2010): 37B25, 46N10, 47J25, 54E50, 54E52, 90C30, 90C48.
