SOME INEQUALITIES ON w*UR MODULUS OF CONVEXITY AND GEOMETRIC PROPERTIES OF BANACH SPACES X AND X

Let X be a Banach space. In this paper, we study the properties of w*UR modulus of convexity of X* respect to x, delta(X)* (epsilon,x), where 0 <= epsilon <= and x is an element of S(X), and the relationship between the values of w*UR modulus and reflexivity, uniform non-squareness and normal structure respectively. Among other results, we proved that if delta(X)*(epsilon,x) > 1/2 - epsilon/4 for all x is an element of S(X), and any 0 < epsilon < 2 then both X and X* have uniform normal structure.