vol. 162, No. 2, 1991 k-β and k-Nearly Uniformly Convex Banach Spaces Denka Kutzarova Different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of Banach spaces. In the present paper we introduce other properties of this type, namely k-β and k-nearly uniform convexity. The definitions, as well as some of the results presented here, are announce...