接近一致凸空间的对偶空间

Abstract

Abstract:

In this paper, we introduce two new classes of Banach spaces: k nearly uniformly smooth spaces and ω nearly uniformly smooth spaces, which are the dual notions to k nearly uniformly convex spaces and ω nearly uniformly convex spaces respectively, introduced by Denka Kutzarova. We give some characters and properties of these two kinds of Banach spaces. Apart from that we really distinguish the k uniformly smooth spaces, k nearly uniformly smooth spaces, ω nearly uniformly smooth spaces, fully k smooth spaces and nearly uniformly smooth spaces.

Key words: k uniformly smooth space, k nearly uniformly smooth space, ω nearly uniformly smooth space, Fully k smooth space, Banach space

CLC Number:

46B09

Suya latu, Wudun qiqige, BAO Laiyou. Banach Spaces which are Dual to k Nearly Uniformly Convex Spaces[J].Acta mathematica scientia,Series A, 2011, 31(3): 805-813.

Trendmd

References

[1] Clarkson J A. Uniformly convex spaces. Trans Amer Math Soc, 1936, 40: 396–414

[2] Sullivan F. A generalization of uniformly rotund Banach spaces. Canad J Math, 1979, 31: 628–636

[3] Suyalatu, Wu C X. k-uniformly rotund spaces and k-uniformly smooth spaces. Chinese Sci Bull, 1998, 43(2): 92–95

[4] Huff R E. Banach spaces which are nearly uniformly convex. Rocky Mountin J Math, 1980, 10: 743–749

[5] Kutzarova D N. k- and k-Nearly uniformly convex Banach spaces. J Math Anal Appl, 1991, 162: 322–338

[6] Sekowski T, Stachura A. Noncompact smoothness and noncompact convexity. Atti Sem Mat Fis Univ Modena, 1988, 36: 329–338

[7] Cao W C. Near smoothness, near convexity and drop property in Banach spaces and its applications. Chin J Math, 1995, 15(2): 187–190

[8] Fan Ky, Glicksburg I. Fully convex normed linear spaces. Proc Nat Acad USA, 1955, 41: 683–698

[9] Nan C X, Wang J H. On the LkUR and LkR spaces. Math Proc Camb Phil Soc, 1988, 104: 521–526

[10] Partington J R. On the Banach-Saks property. Math Proc Camb Phil Soc, 1977, 82: 369–374

[11] Bana´s J. On drop property and nearly uniformly smooth Banach spaces. Nonlinear Analysis, 1990, 14: 927–933

[12] Kutzarova D N, Landes T. NUS and related properties of finite direct sums. Boll U I, 1994, 8A(7): 45–54

[13] Lin B L , Yu X T. On the k-uniform rotund and the fully convex anach spaces. J Math Anal Appl, 1985, 110: 07–410

[14] Suyalatu W, Alatengsubude H, Bao L Y. Some geometric properties related to smoothness of Banach spaces. Nonlinear Analysis, 2007, 66: 723--734

[15] Kutzarova D N. On condition and ∇-uniform convexity. C R Acad Bulgare Sci Carolin Math Phys, 1989: 30(2): 95–98

[16] Kutzarova D N, Lin B L. Locally k-Nearly uniformly convex Banach spaces. Math Balkanica Fasc, 1994, 8(2/3): 203–210

[17] Bana´s J. Compactness conditions in the geometric theory of Banach spaces. Nonlinear Analysis, 1991, 16:

669-682

[18] 杨长森, 左红亮. Hahn-Banach定理在凸性模定义中的应用. 数学物理学报, 2001, 21A(1): 133--137

[19] 方习年, 王建华. 凸性和Banach-Saks性质.数学物理学报, 2002, 22A(3): 297--303

[20] 王建华. 非自反Banach空间中的度量投影. 数学物理学报, 2006, 26A(6): 840--846

[21] 逄宏伟, 苏雅拉图. Banach空间闭超平面上度量投影的连续性. 数学物理学报, 2010, 30A(4): 1138--1143

Banach Spaces which are Dual to k Nearly Uniformly Convex Spaces

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(5): 846-859.
[2]	Yao Yuwu, Chen Xiu, Niu Xin. Distributional Chaos on Complex Sectors [J]. Acta mathematica scientia,Series A, 2017, 37(5): 950-961.
[3]	Cai Gang, Yekini Shehu. Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-Contractions in q-Uniformly Smooth and Uniformly Convex Banach Spaces [J]. Acta mathematica scientia,Series A, 2016, 36(4): 623-638.
[4]	Zeng Chaoying, Suyalatu. QCLkR Spaces and QCLkS Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1080-1088.
[5]	Cai Gang. Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(3): 487-502.
[6]	Liu Yongquan, Guo Weiping. Convergence Theorems of Composite Implied Iterative Scheme for Mixed Type Asymptotically Nonexpansive Mappings [J]. Acta mathematica scientia,Series A, 2015, 35(2): 422-440.
[7]	GUO Wei-Ping, WEN Yi-Hui. Generalized Implicit Complementarity Problems in Banach Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1391-1396.
[8]	XUE Zhi-Qun, LV Gui-Wen. Remarks of Convergence Theorems of Mann Iterative Process with Errors for Φ-Hemicontractive Mappings in Uniformly Smooth Real Banach Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(3): 669-673.
[9]	CAI Gang, BU Shang-Quan. Strong Convergence Theorems of a Modified Mann Iterative Method for Nonexpansive Mappings in Banach Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(1): 1-8.
[10]	YIN Ting-Ting, HU Chang-Song, WU Zhi-Yu. The Fixed Point Theorem of Nonexpansive Mapping [J]. Acta mathematica scientia,Series A, 2013, 33(5): 906-911.
[11]	XIE Sheng-Li, GE Ci-Shui. Existence of Solutions of Nonlocal Terminal Value Problems for Nonlinear Mixed Integro-Differential Equations in Banach Spaces [J]. Acta mathematica scientia,Series A, 2013, 33(3): 550-560.
[12]	ZU Juan. The Roper-Suffridge Extension Operator in Complex Banach Space [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1582-1591.
[13]	YANG Li-Ping, XIE Xiang-Sheng. Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1062-1070.
[14]	FANG Hong-Wei, SU Ya-La-Tu. The Continuity of the Metric Projections on a Close Hyperplane in \|Banach Space [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1138-1143.
[15]	XU Yong-Chun, HE Xin-Feng, HOU Zhi-Bin, HE Zhen. Generalized Projection Methods for Noor Variational Inequalities in Banach Spaces [J]. Acta mathematica scientia,Series A, 2010, 30(3): 808-817.