A Generalization of Uniformly Extremely Convex Banach Spaces

Abstract EN

We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha.

We prove that the new class of Banach spaces lies strictly between either the classes of k-uniformly rotund spaces and k-strongly convex spaces or classes of fully k-convex spaces and k-strongly convex spaces and has no inclusive relation with the class of locally k-uniformly convex spaces.

We obtain in addition some characterizations and properties of this new class of Banach spaces.

In particular, our results contain the main results of Wulede and Ha.