Properties of the Solution Set of a Class of Mixed Variational Inqualities. (22nd November 2022)

• Record Type: Journal Article
• Authors: Xu, Yang; Huang, Zheng-Hai
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1779
• Page End: 1800
• Publication Date: 2022-11-22
• Subjects: Mixed variational inequalities -- nonemptiness and compactness -- solution set -- weakly homogeneous mappings; 90C33 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2135102
• Languages: English
• ISSNs: 0163-0563

Abstract

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.