Hölder Continuity for Solution Mappings of Parametric Non-convex Strong Generalized Ky Fan Inequalities. (17th February 2020)

• Record Type: Journal Article
• Authors: Xu, Yang Dong; Chen, Chun Rong; Fang, Chang Jie
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 3(2020)
• Page Start: 344
• Page End: 360
• Publication Date: 2020-02-17
• Subjects: Hölder continuity -- non-convex separation theorem -- strong generalized Ky Fan inequality; 49K05 -- 90C29; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1628051
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article focuses on a new approach to investigate the Hölder continuity for the solution mapping of a parametric non-convex strong generalized Ky Fan inequality. Based on a non-convex separation theorem, the union relation between the solution set of the parametric non-convex strong generalized Ky Fan inequality and the solution sets of a series of Ky Fan inequalities, is established. Without density results and any information on the solution mapping, a sufficient condition for the Hölder continuity of the solution mapping to the parametric non-convex strong generalized Ky Fan inequality is given by using the key union relation. Our method does not impose any convexity, monotonicity, and the single-valuedness of the solution mapping.