Hausdorff continuity conditions for parametric nonconvex equilibrium problems

This paper focuses on parametric equilibrium problems where the data exhibits nonconvexity but maintains an arcwise connected structure. We begin by investigating the stability of a scalar equilibrium problem, without relying on the convexity of the constraint map or the concavity of the objective function. Next, we establish Hausdorff continuity conditions for approximate (weakly) efficient solution maps to vector equilibrium problems using the linear scalarization method. These approaches provide new insights and methodologies that are applicable even in specific cases of the underlying problems, with promising applications in diverse fields. Through illustrative examples, we demonstrate the applicability and significance of obtained results in comparison to existing ones in the literature