一类多值广义向量似变分不等式解的存在性

A Multiple-valued Generalized Vector Variational-like Inequality

在Banach空间中研究了一类多值广义向量似变分不等式问题(GMLVVIP),此类变分不等式以经典的变分不等式为基础,将单值映射推广到了多值映射.在多值映射与仿射的条件下,利用T的θ-h半连续与伪单调性,通过运用KKM定理和K-F-G不动点定理,证明了这类GMLVVIP解的存在性并给出了证明.

In Banach spaces, a new kind of multiple-valued generalized vector variational-like inequality problem （GMLWIP） is introduced and studied. This kind of variational inequality is based on the classical variational inequality, taking the single-valued mapping to extend the multiple-valued mapping. In the case of multiple-valued mapping and affine, we use hemicontinuity and quasi-monotone of T and show some existence theorems about them by using the KKM-theorem and the K- F-G fixed-point theorem. Our work extends and improves some important known results in Ref[5]. WOldS：