Year 2025,
Volume: 54 Issue: 6, 2237 - 2243, 30.12.2025
Haiying Li
,
Xiangrun Yang
,
Changsen Yang
References
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[1] J. Alonso, P. Martin and P. L. Papini, Wheeling around von Neumann-Jordan constant
in Banach spaces, Studia Math. 188, 135–150, 2008.
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[2] J. A. Clarkson, The von Neumann-Jordan constant for the Lebesgue space, Ann.
Math. 38, 114–115, 1937.
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[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.
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[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.
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[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.
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[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.
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[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.
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[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.
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[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.
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[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.
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[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.
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[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
Haiying Li
,
Xiangrun Yang
,
Changsen Yang
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 $p\geq p_1 \geq1$.
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.