Research Article
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Year 2025, Volume: 54 Issue: 6, 2237 - 2243, 30.12.2025
https://doi.org/10.15672/hujms.1378317

Abstract

Project Number

11771126

References

  • [1] J. Alonso, P. Martin and P. L. Papini, Wheeling around von Neumann-Jordan constant in Banach spaces, Studia Math. 188, 135–150, 2008.
  • [2] J. A. Clarkson, The von Neumann-Jordan constant for the Lebesgue space, Ann. Math. 38, 114–115, 1937.
  • [3] Y. Cui, W. Huang, H. Hudzik and R. Kaczmarek, Generalized von Neumann-Jordan constant and its relationship to the fixed point property, Fixed Point Theory Appl. 40, 1–11, 2015.
  • [4] M. Kato, L. Maligranda and Y. Takahashi, On James and Jordan-von Neumann constant and the normal structure coefficient of Banach spaces, Studia Math. 144, 275–295, 2001.
  • [5] H. Li, X. Yang and C. Yang, On (n, p)-th von Neumann-Jordan constants for Banach spaces, Math. Inequal. Appl. 27 (3), 583-600, 2024.
  • [6] Q. Liu and Y. Li, On a new geometric constant related to the Euler-Langrange type identity in Banach spaces, Mathematics 116, 1–12, 2021.
  • [7] Q. Liu, C. Zhou, M. Sarfraz and Y. Li, On new moduli related to the generalization of the Parallelogram law, Bull. Malays. Math. Sci. Soc. 45, 307–321, 2022.
  • [8] K.-I Mitani, K.-S. Satio, On von Neuman-Jordan constant of generalized Banas- Fr¸aczek spaces II, Linear Nonlinear Anal. 8, 217–223, 2022.
  • [9] K.-I Mitani, K.-S. Satio and Y. Takahashi, On the von Neuman-Jordan constant of generalized Banas-Fr¸aczek spaces, Linear Nonlinear Anal. 2, 311–316, 2016.
  • [10] K. Naoto, K. S. Saito and K. I. Mitani, Extremal structure of the set of absolute norms on $R^{2}$ and the von Neumann-Jordan constant, J. Math. Anal. Appl. 370, 101–106, 2010.
  • [11] F. Wang. On the James and von Neumann-Jordan constants in Banach spaces. Proc. Amer. Math. Soc. 138, 695–701, 2010.
  • [12] C. Yang. Jordan-von Neumann constant for Banas-Fr¸aczek space. Banach J. Math. Anal. 8, 185–192, 2014.
  • [13] C. Yang and H. Li, An inequality between Jordan-von Neumann constant and James constant, Appl. Math. Lett. 23, 227–281, 2010.
  • [14] C. Yang and F. Wang, The von Neumann-Jordan constant for a class of Day-James spaces, Mediterr. J. Math. 13, 1127–1133, 2016.
  • [15] C. Yang and F. Wang, An extension of a simple inequality between von Neumann- Jordan and James constants in Banach spaces, Acta Mathematica Sinica Engl. Ser., 33, 1287–1296, 2017.
  • [16] C. Yang and T. Wang, Generalized von Neumann-Jordan constant $C_{NJ}^{(p)}(X)$ for the regular octagon spaces, Math. Inequal. Appl. 20, 483–490, 2017.
  • [17] C. Yang and X. Yang, On the James type constant and von Neumann-Jordan constant for a class of the Banas-Fraczek space, J. Math. Inequal. 10, 551–558, 2016.
  • [18] X. Yang and C. Yang. An inequality between $L_{YJ}(\lambda,\mu, X)$ constant and generalized James Constant. Math. Inequal. Appl. 27, 571–581, 2024.
  • [19] Z. Zuo and C. Tang, On James and Jordan-von Neumann type constants and normal structure in Banach spaces. Topol. Methods Nonlinear Anal. 49, 615–623, 2017.
  • [20] Z. Zuo, L. Wang, Y. Zhao and Y. Wu. On the generalized von Neumann-Jordan type constant for some concrete Banach spaces. Math. Inequal. Appl. 24, 597–615, 2021.
  • [21] Z. Zuo, Y. Huang and J.Wang, The generalized Gao’s constant of absolute normalized norms in $\mathbb{R}^{2}$. Math. Inequal. Appl. 26, 109–129, 2023.

On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek

Year 2025, Volume: 54 Issue: 6, 2237 - 2243, 30.12.2025
https://doi.org/10.15672/hujms.1378317

Abstract

In this paper, we study the generalized von Neumann-Jordan constant $C^{(p)}_{NJ}(X)$ for the generalized Banas-Fraczek space and improve related results on the Banas-Fraczek space. The exact value of $C^{(p)}_{NJ}(X)$ will be calculated for $X$ to be the generalized Banas-Fraczek space $\mathbb{R}^2_{a,b,p_1}$ in the case $p\geq2$ such that $p_1\geq p\geq2$ or $p\geq p_1 \geq1$.

Project Number

11771126

References

  • [1] J. Alonso, P. Martin and P. L. Papini, Wheeling around von Neumann-Jordan constant in Banach spaces, Studia Math. 188, 135–150, 2008.
  • [2] J. A. Clarkson, The von Neumann-Jordan constant for the Lebesgue space, Ann. Math. 38, 114–115, 1937.
  • [3] Y. Cui, W. Huang, H. Hudzik and R. Kaczmarek, Generalized von Neumann-Jordan constant and its relationship to the fixed point property, Fixed Point Theory Appl. 40, 1–11, 2015.
  • [4] M. Kato, L. Maligranda and Y. Takahashi, On James and Jordan-von Neumann constant and the normal structure coefficient of Banach spaces, Studia Math. 144, 275–295, 2001.
  • [5] H. Li, X. Yang and C. Yang, On (n, p)-th von Neumann-Jordan constants for Banach spaces, Math. Inequal. Appl. 27 (3), 583-600, 2024.
  • [6] Q. Liu and Y. Li, On a new geometric constant related to the Euler-Langrange type identity in Banach spaces, Mathematics 116, 1–12, 2021.
  • [7] Q. Liu, C. Zhou, M. Sarfraz and Y. Li, On new moduli related to the generalization of the Parallelogram law, Bull. Malays. Math. Sci. Soc. 45, 307–321, 2022.
  • [8] K.-I Mitani, K.-S. Satio, On von Neuman-Jordan constant of generalized Banas- Fr¸aczek spaces II, Linear Nonlinear Anal. 8, 217–223, 2022.
  • [9] K.-I Mitani, K.-S. Satio and Y. Takahashi, On the von Neuman-Jordan constant of generalized Banas-Fr¸aczek spaces, Linear Nonlinear Anal. 2, 311–316, 2016.
  • [10] K. Naoto, K. S. Saito and K. I. Mitani, Extremal structure of the set of absolute norms on $R^{2}$ and the von Neumann-Jordan constant, J. Math. Anal. Appl. 370, 101–106, 2010.
  • [11] F. Wang. On the James and von Neumann-Jordan constants in Banach spaces. Proc. Amer. Math. Soc. 138, 695–701, 2010.
  • [12] C. Yang. Jordan-von Neumann constant for Banas-Fr¸aczek space. Banach J. Math. Anal. 8, 185–192, 2014.
  • [13] C. Yang and H. Li, An inequality between Jordan-von Neumann constant and James constant, Appl. Math. Lett. 23, 227–281, 2010.
  • [14] C. Yang and F. Wang, The von Neumann-Jordan constant for a class of Day-James spaces, Mediterr. J. Math. 13, 1127–1133, 2016.
  • [15] C. Yang and F. Wang, An extension of a simple inequality between von Neumann- Jordan and James constants in Banach spaces, Acta Mathematica Sinica Engl. Ser., 33, 1287–1296, 2017.
  • [16] C. Yang and T. Wang, Generalized von Neumann-Jordan constant $C_{NJ}^{(p)}(X)$ for the regular octagon spaces, Math. Inequal. Appl. 20, 483–490, 2017.
  • [17] C. Yang and X. Yang, On the James type constant and von Neumann-Jordan constant for a class of the Banas-Fraczek space, J. Math. Inequal. 10, 551–558, 2016.
  • [18] X. Yang and C. Yang. An inequality between $L_{YJ}(\lambda,\mu, X)$ constant and generalized James Constant. Math. Inequal. Appl. 27, 571–581, 2024.
  • [19] Z. Zuo and C. Tang, On James and Jordan-von Neumann type constants and normal structure in Banach spaces. Topol. Methods Nonlinear Anal. 49, 615–623, 2017.
  • [20] Z. Zuo, L. Wang, Y. Zhao and Y. Wu. On the generalized von Neumann-Jordan type constant for some concrete Banach spaces. Math. Inequal. Appl. 24, 597–615, 2021.
  • [21] Z. Zuo, Y. Huang and J.Wang, The generalized Gao’s constant of absolute normalized norms in $\mathbb{R}^{2}$. Math. Inequal. Appl. 26, 109–129, 2023.
There are 21 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Haiying Li 0009-0001-5860-2982

Xiangrun Yang 0009-0009-1191-0580

Changsen Yang 0000-0002-8333-3390

Project Number 11771126
Submission Date October 19, 2023
Acceptance Date March 6, 2025
Early Pub Date April 11, 2025
Publication Date December 30, 2025
Published in Issue Year 2025 Volume: 54 Issue: 6

Cite

APA Li, H., Yang, X., & Yang, C. (2025). On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek. Hacettepe Journal of Mathematics and Statistics, 54(6), 2237-2243. https://doi.org/10.15672/hujms.1378317
AMA Li H, Yang X, Yang C. On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek. Hacettepe Journal of Mathematics and Statistics. December 2025;54(6):2237-2243. doi:10.15672/hujms.1378317
Chicago Li, Haiying, Xiangrun Yang, and Changsen Yang. “On the Constant ${C^{(p)}_{NJ}(X)}$ for the Generalized Banas-Fraczek”. Hacettepe Journal of Mathematics and Statistics 54, no. 6 (December 2025): 2237-43. https://doi.org/10.15672/hujms.1378317.
EndNote Li H, Yang X, Yang C (December 1, 2025) On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek. Hacettepe Journal of Mathematics and Statistics 54 6 2237–2243.
IEEE H. Li, X. Yang, and C. Yang, “On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 6, pp. 2237–2243, 2025, doi: 10.15672/hujms.1378317.
ISNAD Li, Haiying et al. “On the Constant ${C^{(p)}_{NJ}(X)}$ for the Generalized Banas-Fraczek”. Hacettepe Journal of Mathematics and Statistics 54/6 (December2025), 2237-2243. https://doi.org/10.15672/hujms.1378317.
JAMA Li H, Yang X, Yang C. On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek. Hacettepe Journal of Mathematics and Statistics. 2025;54:2237–2243.
MLA Li, Haiying et al. “On the Constant ${C^{(p)}_{NJ}(X)}$ for the Generalized Banas-Fraczek”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 6, 2025, pp. 2237-43, doi:10.15672/hujms.1378317.
Vancouver Li H, Yang X, Yang C. On the constant ${C^{(p)}_{NJ}(X)}$ for the generalized Banas-Fraczek. Hacettepe Journal of Mathematics and Statistics. 2025;54(6):2237-43.