非对称赋范空间上点到集合的最大距离及最远点的刻画  

The maximum distance from a point to a set in asymmetric normed space and the characterization of the farthest point

作　　者：段华 吴健荣 DUAN Hua;WU Jianrong(School of Mathematics Science,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《苏州科技大学学报（自然科学版）》2024年第1期21-28,共8页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(11971343)。

摘　　要：主要研究了非对称赋范空间上的最远点问题。首先,在非对称赋范空间中引入了最远点及最远点映射的概念,研究了最远点集及最远点映射的基本性质;其次,借助非对称赋范空间对偶空间理论得到了点到非空有界集的最大距离公式;最后,利用拟支撑超平面理论给出了点到非空有界集的最远点的等价刻画。This paper mainly studies the farthest point problem in asymmetric normed space.Firstly,the concepts of the farthest point and the farthest point mapping were introduced in the asymmetric normed space,and the basic properties of the farthest point set and the farthest point mapping were investigated.Secondly,the maximum distance formula from point to non-empty bounded set was derived by means of the dual space theory of asymmetric normed space.Finally,by using the quasi-supported hyperplane,the farthest point from a point to a non-empty bounded set was characterized.

关 键 词：非对称赋范空间 最大距离 最远点 拟支撑超平面 

分 类 号：O177[理学—数学]