Fixed Points, Continuous Selections, and Existence of Solution of Optimization-Related Problems. (2nd January 2018)

• Record Type: Journal Article
• Authors: Khanh, Phan Quoc; Long, Vo Si Trong
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 1(2018)
• Page Start: 100
• Page End: 125
• Publication Date: 2018-01-02
• Subjects: Coincidence points -- continuous selections -- equilibria -- existence of solutions -- fixed points -- GFC-spaces -- quasivariational inclusions -- variational relations; 90C26 -- 90C48 -- 47J22 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1355320
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T -KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.