On Strictly Convex and Strictly Convex According to an Index Semi-Normed Vector Spaces

The purpose of this paper is giving the notion of strictly convex semi-normed vector spaces according to an index and the notion of an extreme point of a convex set C in a vector space X, according to the semi-norm p in the space X. We extend to semi-normed vector spaces, via semi-pre-inner-products, some known results on strictly convex normed vector spaces, which are characterized in terms of semi-inner-products.