数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 369-378.doi: 10.1007/s10473-020-0205-7

• 论文 • 上一篇    下一篇

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

张子厚1, Vicente MONTESINOS2, 刘春燕1   

  1. 1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
    2. Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, C/Vera, s/n, 46022 Valencia, Spain
  • 收稿日期:2018-03-16 修回日期:2019-03-20 出版日期:2020-04-25 发布日期:2020-05-26
  • 通讯作者: Vicente MONTESINOS E-mail:vmontesinos@mat.upv.es
  • 作者简介:Zihou ZHANG,E-mail:zhz@sues.edu.cn;Chunyan LIU,E-mail:chyliu001@yahoo.com.cn
  • 基金资助:
    The first named author was supported in part by the National Natural Science Foundation of China (11671252, 11771248); The second named author is supported by Proyecto MTM2014-57838-C2-2-P (Spain) and the Universitat Politècnica de València (Spain).

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

Zihou ZHANG1, Vicente MONTESINOS2, Chunyan LIU1   

  1. 1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
    2. Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, C/Vera, s/n, 46022 Valencia, Spain
  • Received:2018-03-16 Revised:2019-03-20 Online:2020-04-25 Published:2020-05-26
  • Contact: Vicente MONTESINOS E-mail:vmontesinos@mat.upv.es
  • Supported by:
    The first named author was supported in part by the National Natural Science Foundation of China (11671252, 11771248); The second named author is supported by Proyecto MTM2014-57838-C2-2-P (Spain) and the Universitat Politècnica de València (Spain).

摘要: We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points, related to the so-called Rolewicz's property (α). We give a characterization of those points in terms of continuity properties of the identity mapping. The connection between these two geometric properties is established, and finally an application to approximative compactness is given.

关键词: Banach spaces, nearly strongly convex spaces, nearly very convex spaces, Kadec property, Radon-Riesz property, approximative compactness

Abstract: We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points, related to the so-called Rolewicz's property (α). We give a characterization of those points in terms of continuity properties of the identity mapping. The connection between these two geometric properties is established, and finally an application to approximative compactness is given.

Key words: Banach spaces, nearly strongly convex spaces, nearly very convex spaces, Kadec property, Radon-Riesz property, approximative compactness

中图分类号: 

  • 46B20