Derivatives of generalized farthest functions and existence of generalized farthest points
For a real Banach space \(X\), the relationship between directional derivatives of generalized farthest functions and the existence of generalized farthest points in Banach spaces is investigated. It is proved that a generalized farthest function generated by a bounded closed set having a one-sided directional derivative equal to 1 or~\(-1\) implies the existence of generalized farthest points. New characterization theorems of (compact) locally uniform convex sets are given. This paper continues investigations by F.S.~DeBlasi and J.~Myjak, C.~Li, and R.~Ni.
scientific article; zbMATH DE number 5016207
scientific article