Absolute Norms on n 1

In this paper, we study the absolute normalized norms on n. We show that the set of all absolute normalized norms on n is in one-to-one correspondence with the set nof all continuous convex functions on nwith some suitable conditions, where n Ž s1, . . . , sn 1. n 1; s1 s2 sn 1 1, si 0 Ž1 i n 1.4. As some applications, we show that an absolute norm on n is strictly convex if and only if the corresponding function on n is strictly convex. Further, we consider the von Neumann Jordan constant of n with an absolute normalized norm.