Convexity of generalized proximinal sets in Banach spaces. (2nd September 2018) - Luo, Xian-Fa; Li, Chong; Peng, Lihui; Yao, Jen-Chih
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.