Convexity of generalized proximinal sets in Banach spaces. (2nd September 2018)

• Record Type: Journal Article
• Authors: Luo, Xian-Fa; Li, Chong; Peng, Lihui; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 67:Number 9(2018)
• Page Start: 1535
• Page End: 1551
• Publication Date: 2018-09-02
• Subjects: Generalized best approximation -- proximinal set -- weakly uniform convexity -- compactly locally uniform convexity; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1480626
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: For a bounded closed convex subset C of a Banach space X with the origin as an interior point, we study the convexity issue of proximinal sets G in Banach spaces in the sense of generalized best approximation determined by the Minkowski functional generated by C . Some sufficient conditions such as the smoothness and compactly locally uniform convexity of C, or the weakly uniform convexity of are provided for a proximinal set G to be convex.