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<p>Based on the three-parameter generalized parallelogram law, this article introduces two new geometric constants in Banach spaces. Since these constants involve three parameters, they incorporate several classical geometric constants. For the first constant, multiple equivalent forms are derived, and its values in specific spaces are computed. Subsequently, by restricting the variables of the first constant to the unit sphere, the second constant is obtained, and its relationships with other constants are comparatively analyzed. Finally, the intrinsic connections between these constants and the uniform non-squareness as well as the normal structure of Banach spaces are further investigated.</p>

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On (α, β, γ) von Neumann-Jordan type constants in Banach spaces

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Shuoyi Wan,
  • Qi Liu,
  • Mengmeng Bao,
  • Yuxin Wang

摘要

Based on the three-parameter generalized parallelogram law, this article introduces two new geometric constants in Banach spaces. Since these constants involve three parameters, they incorporate several classical geometric constants. For the first constant, multiple equivalent forms are derived, and its values in specific spaces are computed. Subsequently, by restricting the variables of the first constant to the unit sphere, the second constant is obtained, and its relationships with other constants are comparatively analyzed. Finally, the intrinsic connections between these constants and the uniform non-squareness as well as the normal structure of Banach spaces are further investigated.