Convexity and Proximinality in Banach Space - Z. H. Zhang; C. Y. Liu (Journal of Function Spaces and Applications)
By the continuity of preduality map, we give some necessary and sufficient conditions of the strongly convex and very convex spaces, respectively. Using nearly strong convexity of 𝑋, we give some equivalent conditions that every element in 𝑋 is strongly unique of order 𝑝, bounded strongly unique of order 𝑝, and locally strongly unique of order 𝑝.