参数广义弱向量拟平衡问题解映射的H-连续性刻画

研究了Hausdorff拓扑向量空间中的一类参数广义弱向量拟平衡问题(PGWVQEP)的稳定性.首先,给出了此问题的参数间隙函数,研究了参数间隙函数的连续性.然后,提出了一个与参数间隙函数相关的关键假设,讨论了它的连续性,并给出关键假设的等价刻画.最后,借助于假设,获得了PGWVQEP解映射Hausdorff半连续的充分必要条件.并举例验证了所得结果.

Characterizations of H Continuity for Solution Mapping to Parametric Generalized Weak Vector Quasi Equilibrium Problems

The stability of a class of parametric generalized weak vector quasi-equilibrium problems (PGWVQEP) in Hausdorff topological vector spaces, were studied. First, a parametric gap function for the problem was given, and the continuity property of the function was studied. Next, a key hypothesis related to the gap function for the considered problem was presented, the characterizations of this hypothesis were discussed, and an equivalence theorem for the key hypothesis was given. Finally, by means of the hypothesis, the sufficient and necessary conditions for the Hausdorff semicontinuity of the solution mapping to PGWVQEP were obtained. Examples were given to verify the obtained results.