In this paper, the Hausdorff quasi-upper and Hausdorff quasi-lower semicontinuity for set-valued mappings are introduced to derive the upper semicontinuity and lower semicontinuity of cone constraint mapping in normed vector spaces. We discuss existence of solutions for generalized vector equilibrium problems with cone constraints. Moreover, we establish the lower semicontinuity of (weakly) efficient approximate solution mappings, upper semicontinuity of weakly efficient approximate solution mappings, and Hausdorff upper semicontinuity of efficient approximate solution mappings to parametric generalized vector equilibrium problems with cone constraints under some suitable conditions. Some examples are also given to illustrate our main results.

本文引入集值映射的Hausdorff拟上半连续性和Hausdorff拟下半连续性，推导了范数向量空间中锥约束映射的上半连续性和下半连续性。我们讨论了具有锥约束的广义向量平衡问题的解的存在性。此外，我们建立了（弱）有效近似解映射的下半连续性、弱有效近似解映射的上半连续性和有效近似解映射的Hausdorff上半连续性，以在一些合适的条件下具有锥约束的参数广义向量平衡问题。还给出了一些例子来说明我们的主要结果。