Semicontinuity of approximate solution mappings for parametric generalized weak vector equilibrium problems

In this paper, we first introduce a new setvalued mapping by the scalar approximate solution mapping of a parametric generalized weak vector equilibrium problem and obtain some of its properties. By one of obtained properties, we establish the lower semicontinuity the approximate solution mapping to a parametric generalized weak vector equilibrium problem without the assumptions about monotonicity and approximate solution mappings. Simultaneously, under some suitable conditions, we obtain the upper semicontinuity of the approximate solution mapping to a generalized parametric weak vector equilibrium problem. Our main results improve and extend the corresponding ones in the literature.