Some inequalities concerning the James constant in Banach spaces

Let A 2 ( X ) be the constant introduced by Baronti, Casini and Papini. This paper discusses the constant A 2 ( X ) and states an estimate A 2 ( X ) ⩽ 1 + J ( X ) − 1 in terms of the James constant. The estimate enables us to improve an inequality between the James and von Neumann–Jordan constants.