Some Metric and Topological Properties of Nearly Strongly and Nearly Very Convex Spaces

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 betw...

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Bibliographic Details
Published inActa mathematica scientia Vol. 40; no. 2; pp. 369 - 378
Main Authors Zhang, Zihou, Montesinos, Vicente, Liu, Chunyan
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.03.2020
School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China%Instituto de Matemática Pura y Aplicada,Universitat Politècnica de València,C/Vera,s/n,46022 Valencia,Spain
Subjects
Analysis
Mathematics
Mathematics and Statistics
approximative compactness
Radon-Riesz property
41A65
Kadec property
46B20
Banach spaces
nearly strongly convex spaces
nearly very convex spaces
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Summary: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.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-020-0205-7