### Porosity-based methods for solving stochastic feasibility problems

#### Abstract

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

#### Full Text:

PDFDOI: http://dx.doi.org/10.24193/subbmath.2022.1.01

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