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

作　　者：李珊珊 崔云安 LI Shan-shan;CUI Yun-an(School of Sciences, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第6期153-156,共4页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

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。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.

关 键 词：2-范数线性空间 压缩映像原理 不动点 严格凸 一致凸 

分 类 号：O177.3[理学—数学]