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

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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.

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Acknowledgements

The second named author wants to thank the School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, for its hospitality and the wonderful working conditions provided.

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Authors and Affiliations

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

    Zihou Zhang & Chunyan Liu

  2. Instituto de Matemática Pura y Aplicada, Universitat Politècnica de València, C/Vera, s/n, 46022, Valencia, Spain

    Vicente Montesinos

Authors
  1. Zihou Zhang
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  2. Vicente Montesinos
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  3. Chunyan Liu
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Corresponding author

Correspondence to Vicente Montesinos.

Additional information

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).

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Zhang, Z., Montesinos, V. & Liu, C. Some Metric and Topological Properties of Nearly Strongly and Nearly Very Convex Spaces. Acta Math Sci 40, 369–378 (2020). https://doi.org/10.1007/s10473-020-0205-7

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  • DOI: https://doi.org/10.1007/s10473-020-0205-7

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