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Geometric properties and continuity of the pre-duality mapping in Banach space

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We use the preduality mapping in proving characterizations of some geometric properties of Banach spaces. In particular, those include nearly strongly convexity, nearly uniform convexity—a property introduced by K. Goebel and T. Sekowski—, and nearly very convexity.

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Acknowledgments

We thank a referee for the careful reading of the manuscript. His/her observations substantially improved the overall aspect of the present work, detected several misprints and made some convenient changes. This work was supported by: (1) The National Natural Science Foundation of China (Grant no. 11271248). (2) Specific Academic Discipline Project of Shanghai Municipal Education Commission (Grant no. B-8932-13-0136). (3) Project MTM2011-22417, Ministerio de Ciencia e Innovación, Spain (V. Montesinos).

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Authors and Affiliations

  1. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201600, People’s Republic of China

    Z. H. Zhang & C. Y. Liu

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

    Vicente Montesinos

  3. Department of Mathematics, Anhui Normal University, Wuhu, 241003, People’s Republic of China

    W. Z. Gong

Authors
  1. Z. H. Zhang
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  2. Vicente Montesinos
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  3. C. Y. Liu
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  4. W. Z. Gong
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Correspondence to Vicente Montesinos.

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Zhang, Z.H., Montesinos, V., Liu, C.Y. et al. Geometric properties and continuity of the pre-duality mapping in Banach space. RACSAM 109, 407–416 (2015). https://doi.org/10.1007/s13398-014-0190-6

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  • DOI: https://doi.org/10.1007/s13398-014-0190-6

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