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Banas–Hajnosz–Wedrychowicz type modulus of convexity and normal structure in Banach spaces

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Abstract

In this paper, we present some sufficient conditions for which the Banach space X has uniform normal structure in terms of the Banas–Hajnosz–Wedrychowicz type modulus of convexity \(SY_X(\epsilon )\), the coefficient of weak orthogonality \(\omega (X)\) and the Domínguez–Benavides coefficient R(1, X). Some known results are improved and strengthened.

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Acknowledgements

This research was partially supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ1601006), the Chongqing New-star Plan of Science and Technology (KJXX2017012), the Scientific Technological Research Program of the Chongqing Three Gorges University (no. 16PY11), the Chongqing Municipal Key Laboratory of Institutions of Higher Education (Grant no. [2017]3), and the Program of Chongqing Development and Reform Commission (Grant no. 2017[1007]), the Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Georges University.

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  1. Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, Chongqing, People’s Republic of China

    Zhan-fei Zuo

  2. Key Laboratory of Intelligent Information Processing and Control, School of Computer Science and Engineering, Chongqing Three Gorges University, Wanzhou, 404100, Chongqing, People’s Republic of China

    Zhan-fei Zuo

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Zuo, Zf. Banas–Hajnosz–Wedrychowicz type modulus of convexity and normal structure in Banach spaces. J. Fixed Point Theory Appl. 20, 58 (2018). https://doi.org/10.1007/s11784-018-0537-2

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  • DOI: https://doi.org/10.1007/s11784-018-0537-2

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