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

doi:10.1007/s10473-020-0205-7

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (2): 369-378.doi: 10.1007/s10473-020-0205-7

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

Zihou ZHANG¹, Vicente MONTESINOS², Chunyan LIU¹

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).

Abstract

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

CLC Number:

46B20

Zihou ZHANG, Vicente MONTESINOS, Chunyan LIU. SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES[J].Acta mathematica scientia,Series B, 2020, 40(2): 369-378.

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

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