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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 2

Skew generalized von Neumann-Jordan constant in Banach spaces

Qichuan Ni(Anqing Normal University)0009-0001-8931-369X
Qi Liu(Anqing Normal University)0000-0003-4322-308X
Yin Zhou(Anqing Normal University)0009-0003-4866-8704
Pages
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Publication Date
2025-04-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, some sufficient conditions for the uniform normal structure associated with the constant $C^{p}_{NJ}(\zeta,\eta,X)$ are established.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a new geometric constant $C^{p}_{NJ}(\zeta,\eta,X)$ in Banach spaces, which is called the skew generalized von Neumann-Jordan constant.
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Key Findings & Data:First, the upper and lower bounds of the new constant are given for any Banach space.
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Conclusion & Impact:Finally, some sufficient conditions for the uniform normal structure associated with the constant $C^{p}_{NJ}(\zeta,\eta,X)$ are established.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:geometric constant · Banach spaces · James constant

Abstract

We introduce a new geometric constant $C^{p}_{NJ}(\zeta,\eta,X)$ in Banach spaces, which is called the skew generalized von Neumann-Jordan constant. First, the upper and lower bounds of the new constant are given for any Banach space. Then we calculate the constant values for some particular spaces. On this basis, we discuss the relation between the constant $C^{p}_{NJ}(\zeta,\eta,X)$ and the convexity modules $\delta_X(\varepsilon)$, the James constant $J(X)$. Finally, some sufficient conditions for the uniform normal structure associated with the constant $C^{p}_{NJ}(\zeta,\eta,X)$ are established.

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Cite This Article

Ni, Q., Liu, Q., Zhou, Y. (2025). Skew generalized von Neumann-Jordan constant in Banach spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 2. https://doi.org/10.15672/hujms.1451136

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