SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

• Published in: 数学物理学报（英文版） Vol. 42; no. 4; pp. 1621 - 1630
• Main Authors: Zihou ZHANG, Yu ZHOU, Chunyan LIU, Jing ZHOU
• Format: Journal Article
• Language: English
• Published: School of Mathematics Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China 2022
• Subjects: τ-strong proximinality,proximinality; Cheby-shev set,nearly strong convexity; nearly strict convexity; k-strict convexity; Approximative τ-compactness; k-strong convexity
• ISSN: 0252-9602; 1572-9087
• DOI: 10.3969/j.issn.0252-9602.2022.04.019

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