A New Characterization of Uniformly Nonsquare Banach Spaces
Donghai Ji · Harbin Ligong Daxue xuebao · 2011
In order to study the relation between heights of unit equilateral triangles and geometric properties of the underlying space,a new geometric constant h(X) is introduced via geometric method.The lower bound of h(X)is presented.It is proved that a Banach space X is uniformly nonsquare if and only if the inequality h(X)1/2 holds,and that a Banach space X has the fixed point property for nonexpansive mappings whenever the inequality h(X)1/2 holds.