Abstract
In this paper, the notions of the Levitin-Polyak well-posedness by perturbations for system of general variational inclusion and disclusion problems (shortly, (SGVI) and (SGVDI)) are introduced in Hausdorff topological vector spaces. Some sufficient and necessary conditions of the Levitin-Polyak well-posedness by perturbations for (SGVI) (resp., (SGVDI)) are derived under some suitable conditions. We also explore some relations among the Levitin-Polyak well-posedness by perturbations, the existence and uniqueness of solution of (SGVI) and (SGVDI), respectively. Finally, the lower (upper) semicontinuity of the approximate solution mappings of (SGVI) and (SGVDI) are established via the Levitin-Polyak well-posedness by perturbations.
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