Properties of the Solution Set of a Class of Mixed Variational Inqualities

Abstract

In this paper, we investigate a class of mixed variational inequalities on nonempty closed convex subsets of real Euclidean spaces. One of the mappings involved is lower semicontinuous and the other is weakly homogeneous. After discussing the boundedness for the solution set (if it is nonempty) of the problem, we focus on the nonemptiness and compactness of the solution set. Two new results on the nonemptiness and compactness of the solution set of the problem are established, and some examples are used to compare the results with those in the literature. It can be seen that new results improve some known related results.

Keywords:

• Mixed variational inequalities
• nonemptiness and compactness
• solution set
• weakly homogeneous mappings

AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 90C30

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant [No 11871051].