2-范数线性空间的严格凸与一致凸性

Strict Convexity and Uniform Convexity in Linear 2-normed Spaces

2-范数线性空间是赋范线性空间的推广,它定义了更为广泛地范数。首先证明了2-范数线性空间中的压缩映像原理是成立的,以及严格凸的2-范数线性空间中的非扩张映射的不动点集是凸集;得到了有限维严格凸的2-范数线性空间是一致凸的,并证明了由向量积诱导的2-范数线性空间是一致凸的。

Linear 2-normed space is a generalization of linear normed space,which defines a more extensive norm.In this paper,we get contraction mapping theorem in linear 2-normed space holds,and the set of fixed points for nonexpansive mapping is convex when linear 2-normed space is strictly convex.We obtain that the strictly convex linear 2-normed space with finite dimension is uniformly convex.Thus we get the corollary that the linear 2-normed space induced by the vector product is uniformly convex.