SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

doi:10.1007/s10473-022-0419-y

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1621-1630.doi: 10.1007/s10473-022-0419-y

SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

张子厚, 周宇, 刘春燕, 周晶

School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

收稿日期:2021-03-17 修回日期:2021-07-18 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Chunyan LIU,E-mail:cyl@sues.edu.cn E-mail:cyl@sues.edu.cn
基金资助:
Zihou Zhang is supported by the National Natural Science Foundation of China (11671252), Yu Zhou is supported by the National Natural Science Foundation of China (11771278).

SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

Zihou ZHANG, Yu ZHOU, Chunyan LIU, Jing ZHOU

School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

Received:2021-03-17 Revised:2021-07-18 Online:2022-08-25 Published:2022-08-23
Contact: Chunyan LIU,E-mail:cyl@sues.edu.cn E-mail:cyl@sues.edu.cn
Supported by:
Zihou Zhang is supported by the National Natural Science Foundation of China (11671252), Yu Zhou is supported by the National Natural Science Foundation of China (11771278).

摘要/Abstract

摘要： In this paper, we discuss the relation between $\tau$-strongly Chebyshev, approximatively $\tau$-compact $k$-Chebyshev, approximatively $\tau$-compact, $\tau$-strongly proximinal and proximinal sets, where $\tau$ is the norm or the weak topology. We give some equivalent conditions regarding the above proximinality. Furthermore, we also propose the necessary and sufficient conditions that a half-space is $\tau$-strongly proximinal, approximatively $\tau$-compact and $\tau$-strongly Chebyshev.

关键词: Approximative $\tau$-compactness, $\tau$-strong proximinality, proximinality, Chebyshev set, nearly strong convexity, $k$-strong convexity, $k$-strict convexity, nearly strict convexity

Abstract: In this paper, we discuss the relation between $\tau$-strongly Chebyshev, approximatively $\tau$-compact $k$-Chebyshev, approximatively $\tau$-compact, $\tau$-strongly proximinal and proximinal sets, where $\tau$ is the norm or the weak topology. We give some equivalent conditions regarding the above proximinality. Furthermore, we also propose the necessary and sufficient conditions that a half-space is $\tau$-strongly proximinal, approximatively $\tau$-compact and $\tau$-strongly Chebyshev.

Key words: Approximative $\tau$-compactness, $\tau$-strong proximinality, proximinality, Chebyshev set, nearly strong convexity, $k$-strong convexity, $k$-strict convexity, nearly strict convexity

中图分类号:

41A65

张子厚, 周宇, 刘春燕, 周晶. SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES[J]. 数学物理学报(英文版), 2022, 42(4): 1621-1630.

Zihou ZHANG, Yu ZHOU, Chunyan LIU, Jing ZHOU. SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1621-1630.

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SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

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