SOME PROPERTIES OF B-CONVEXITY.

In this paper, we give a characteristic of B-convexity structures of finite dimensional B-spaces: if a finite dimensional B-space has the weak selection property then its B-convexity structure satisfies H-condition. We also get some relationships among B-convexity structures, selection property and fixed point property. We show that in a compact convex subset of a finite dimensional B-space satisfying H-condition the weak selection property implies the fixed point property. [ABSTRACT FROM AUTHOR]