广义集值向量变分不等式的例外簇

利用例外簇的概念来研究变分不等式问题解的存在性的方法已变得十分流行.许多学者提出了各类例外簇的概念,并在此概念的基础上利用拓扑度或不动点理论得出许多变分不等式问题解的存在性的相关结论.但是这些研究仅限于单值变分不等式,而对于集值变分不等式的研究很少.因此针对Banach空间中广义集值向量变分不等式解存在性问题,提出了一类C-例外簇概念,并给出相应的解的存在性定理,得到择一型"广义集值向量变分不等式问题有解,否则存在C-例外簇".

Exceptional Family Elements for Set-Valued Mapping of Generalized Vector Variational Inequalities

Recently,the notion of exceptional family elements has become a very promising tool to investigate the solvability of variational inequality problems.Many scholars proposed various types of notions of exceptional family elements to handle the solvability of variational inequality problems by using topological degree theory or fixed point theory.However,these studies focus mostly on single-valued variational inequality problems rather than set-valued types.In order to study the solution to existing problems of generalized set-valued vector variational inequality in Banach space,a kind of C-exceptional family elements is introduced.The corresponding existence theorem is given,and thus an alternative conclusion of "generalized vector variational inequality has a solution,otherwise there exists α C-exceptional family elements" is obtained.