Painlevé-Kuratowski stability of the solution sets to perturbed vector generalized systems (Q1753359)

In the paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, the authors introduce the concepts of problems: a vector-generalize system \((VGS)\) and a sequence of vector-generalize systems \((VGS)_n\). Then, without the assumption of \(C\)-strict monotonicity, they establish the Painlevé-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution sets of the generalized system \((VGS)_n\) by perturbing the feasible set and the objective function in both the given space and its image space. Finally, the density and Painlevé-Kuratowski convergence results of efficient solution sets by virtue of gamma convergence are obtained. Some examples are also given to illustrate these results.