Semicontinuity of approximate solution mappings for parametric generalized weak vector equilibrium problems
Qilin Wang, Xiaobing Li, Jing Zeng · The Journal of Nonlinear Sciences and Applications · 2017
In this paper, we first introduce a new set-valued 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.