PDF(440 KB)
PDF(440 KB)
PDF(440 KB)
Banach空间中的Jordan-von Neumann型常数和正规结构
On Jordan-von Neumann Type Constants and Normal Structure in Banach Spaces
首先利用James常数J（X）给出了Jordan-von Neumann 型常数C-∞（X）的一个估计式，然后由此式说明确实存在C-∞（X）<CZ（X）的例子，最后利用C-∞（X）和 Benavides 常数R（a，X）的关系，得到了空间具有正规结构的充分条件，并通过一些例子说明我们的结论严格推广了一些文献中的结果.
The relationship between James constant J(X) and the Jordan-von Neumann type constant C-∞(X) is given to show there exists a example such that C-∞(X)< CZ(X). Moreover, some sufficient conditions for normal structure in terms of the constant C-∞(X) and the Benavides constant R(a, X) are presented. These results improve some known results.
Jordan-von Neumann型常数 / James常数 / 正规结构 {{custom_keyword}} /
Jordan-von Neumann type constant / James constant / normal structure {{custom_keyword}} /
[1] Alonso J., Llorens-Fuster E., Geometric mean and triangles inscribed in a semicircle in Banach spaces, J. Math. Anal. Appl., 2008, 340(2):1271-1283.
[2] Bynum W., Normal structure coefficients for Banach spaces, Pacific J. Math., 1980, 86(2):427-436.
[3] Domínguez Benavides T., A geometrical coefficient implying the fixed point property and stability results, Houston J. Math., 1996, 22(4):835-849.
[4] Gao J., Lau K. S., On two classes of Banach spaces with uniform normal structure, Studia Math., 1991, 99(1):41-56.
[5] Gao J., A Pythagorean approach in Banach spaces, Journal of Inequalities and Applications, 2006, 2006(1):1-11.
[6] Goebel K., Kirk W. A., Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math., Cambridge Univ. Press, Cambridge, 1990.
[7] Jiménez-Melado A., Llorens-Fuster E., Saejung S., The von Newman-Jordan constant, weak orthogonality and norm al structure in Banach spaces, Proc. Amer. Math. Soc., 2006, 134(2):355-364.
[8] Kato M., Maligranda L., Takahashi Y., On James and Jordan-von Neumann constants and normal structure coefficient of Banach spaces, Studia Math., 2001, 144(3):275-295.
[9] Kirk W. A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 1965, 72(9):1004-1006.
[10] Llorens-Fuster E., Mazcuñán-Navarr E. M., Reich S., The Ptolemy and Zb?ganu constants of normed spaces, Nonlinear Anal., 2010, 72(11):3984-3993.
[11] Mazcuñán-Navarro E. M., Banach spaces properties sufficient for normal structure, J. Math. Anal. Appl., 2008, 337(1):197-218.
[12] Takahashi Y., Some geometric constants of Banach spaces-a unified approach, in:Banach and Function Spaces II, Proc. International Symposium (ISBFS 2006) held in Kitakyushu (Sept. 2006:14-17), Edited by Mikio Kato and Lech Maligranda, Yokohama Publ., Yokohama 2008:191-220.
[13] Yang C. S., Wang F. H., On a new geometric constant related to the von Neumann-Jordan constant, J. Math. Anal. Appl., 2006, 324(1):555-565.
[14] Yang C. S., Wang Y. M., Some properties on von Neumann-Jordan type constant of Banach spaces, Acta Math. Sci., 2012, 32A(1):212-221.
[15] Zb?ganu G., An inequality of M. Radulescu and S. Radulescu which characterizes the inner product spaces, Rev. Roumaine Math. Pures Appl., 2002, 47(2):253-257.
[16] Zuo Z. F., Cui Y. A., Some modulus and normal structure in Banach space, J. Inequal. Appl., 2009, 2009(1):1-15.
[17] Zuo Z. F., Tang C. L., Jordan-von Neumann type constant and fixed points for multivalued nonexpansive mappings, J. Math. Inequal., 2016, 10(3):649-657.
重庆市基础与前沿研究计划（cstc2014jcyjA00022）；重庆市教委科学技术研究项目（KJ1601006）；重庆三峡学院科学研究重点项目（14ZD09）；重庆三峡学院非线性科学与系统结构实验室项目
/
| 〈 |
|
〉 |
