Continuity of the efficient solution mapping for vector optimization problems

This paper aims at investigating the continuity of the efficient solution mapping of perturbed vector optimization problems. First, we introduce the concept of the level mapping. We give sufficient conditions for the upper semicontinuity and the lower semicontinuity of the level mapping. The upper semicontinuity and the lower semicontinuity of the efficient solution mapping are established by using the continuity properties of the level mapping. We establish a corollary about the lower semicontinuity of the minimal point set-valued mapping. Meanwhile, we give some examples to illustrate that the corollary is different from the ones in the literature.