NORMAL STRUCTURE AND POLYGONS IN BANACH SPACES

Abstract

Let X be a Banach space with the unit sphere S(X). In this paper, we study theinscribed isosceles triangles, parallelograms and circumscribed hexagons in S(X). The relationships of these polygons with normal structure, uniformly non-square and other geometric properties are obtained. Some existing results about fixed points and normal structure are improved.