Painlevé-Kuratowski convergence for set optimization solutions using improvement sets

This paper investigates the Painlevé-Kuratowski convergence of solution sets in set optimization problems under perturbations. By introducing the notion of [Formula: see text]-[Formula: see text]-Strictly quasiconvexity for set-valued mappings, we establish sufficient conditions ensuring Painlevé-Kuratowski convergence results of (weak) [Formula: see text]-[Formula: see text]-solutions sets when both the improvement set and the feasible set are subject to perturbations. The theoretical results are illustrated with concrete examples to verify their validity and applicability. These findings contribute to the stability analysis of set optimization and provide a theoretical foundation for handling solution sensitivity in variational and equilibrium problems involving set-valued structures.