On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces

Some relations between the James (or non-square) constant J(X) and the Jord an-von Neumann constant C-NJ(X), and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are;g iven as an answer to a problem of Gao and Lau [16]. Connections between C-N J(X) and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the C-NJ(X)-constant, which implies that a Banach spa ce with C-NJ(X)-constant less than 5/4 has the fixed point property.