General theorems of the Knaster-Kuratowski- Mazurkiewicz type and applications to the existence study in optimization. (1st December 2020)

• Record Type: Journal Article
• Authors: Khanh, Phan Quoc; Long, Vo Si Trong
• Is Part Of: Optimization. Volume 69:Number 12(2020)
• Page Start: 2695
• Page End: 2717
• Publication Date: 2020-12-01
• Subjects: Theorems of the KKM type -- general KKM maps -- alternative theorems -- minimax inequalities -- variational relation problems -- variational inequalities; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1736069
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We establish theorems of the Knaster-Kuratowski-Mazurkiewicz (KKM) type on topological spaces with topologically-based generalized convex structures and apply them to the existence study for variational relation problems, variational inequalities, minimax inequalities and saddle points, and to alternative theorems. Our first main KKM-type theorem is a necessary and sufficient condition, not only a sufficient one as usual. The results improve and extend corresponding contributions in the literature in many aspects.