作者:李珊珊,崔云安
Authors:LI Shan-shan,CUI Yun-an摘要:摘要: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。
Abstract:Abstract: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.

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