The generalized von Neumann--Jordan constant and normal structure in Banach spaces

Abstract

Recently, a new geometric constant called generalized von Neumann--Jordan constant was introduced. In this paper, the relationships between above constant and generalized García--Falset coefficient are given. In terms of this constant, the lower bounds for the weakly convergent sequence coefficient of a Banach space $X$ are also shown. Moreover, some sufficient conditions which imply normal structure and uniform normal structure are presented.