Banach空间中的一个新算子-kUKK算子
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摘要
为了研究Banach空间中的一些几何性质,给出一个新的几何性质kUKK,根据其定义给出了kNUC算子和kUKK算子的定义;证明了kNUC算子与kUKK算子的关系;Banach空间中的算子是kNUC的充要条件是自反且T为kUKK;讨论了kUKK算子的性质,最后研究了kUKK算子与具有kUKK性质之间的关系。
In order to study some geometric properties in Banach space, a new geometric property kUKK is given. The definition of kUKK operator and kNUC operator is given according to its definition.The relation between kUKK operator and kNUC operator is proved. The sufficient and necessary conditions for the operator in Banach space to be kNUC are reflexive and kUKK; The properties of kUKK operators are discussed. Finally, the relationship between kUKK operators and kUKK properties is studied.
In order to study some geometric properties in Banach space, a new geometric property kUKK is given. The definition of kUKK operator and kNUC operator is given according to its definition.The relation between kUKK operator and kNUC operator is proved. The sufficient and necessary conditions for the operator in Banach space to be kNUC are reflexive and kUKK; The properties of kUKK operators are discussed. Finally, the relationship between kUKK operators and kUKK properties is studied.
引文
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[20] 刘红玉.Banach不动点定理的推广及应用[J].广东石油化工学院学报,2015(3):75.
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[2] 刘臣伟.自反空间的性质和应用[J].贵州科学,2015,33(4):9.
[3] 崔云安.Banach空间几何理论及应用[M].北京:科学出版社,2010.
[4] 俞鑫泰.Banach空间几何理论[M].上海:华东师范大学出版社,1986:233.
[5] 定光桂.巴拿赫空间引论[M].北京:科学出版社,1984.
[6] 张恭庆,林源渠.泛函分析讲义[M].北京:北京大学出版社,1987.
[7] HUFF R.Banach Spaces Which are Nearly Uniformly Convex[J].Rocky Montain J Math,1980,10(4):43.
[8] 苏雅拉图,乌敦其其格,包来友.k接近一致凸空间的对偶空间.数学物理学报,2011,31(A3):805.
[9] J.GARCIA-FALSET.Journal of Functional Analysis[J].2006,233:494.
[10] 方习年,王建华.凸性和Banach-Saks性质[J].数学物理学报,2002,22(A3):297.
[11] 徐洪坤.(NUC)空间的一种推广[J].上海第二工业大学学报,1986(1):27.
[12] GARCIA-FALSET J.The Fixed Point Property in Banach Spaces with NUS Property[J].J.Math Anal,1997(215):532.
[13] KUTZAROVA D N,LIN B L.Locally k-Nearly Uniformly Convex Banach Spaces[J].Math Balkanica Fasc,1994,8(2/3):203.
[14] 段丽芬,庄彩彩.赋广义Orlicz范数的Orlicz序列空间的UKK性质[J].通化师范学院学报,2014(4):15.
[15] CLARKSON J.A.Uniformly Convex Spaces[J].Trans.Amer.Math.Soc,1936,40:396.
[16] AMOUCH M.A Spectral Analysis of Linear Operator Pencils on Banach Spaces with Application to Quotient of Bounded Operators[J].International Journal of Analysis & Applications,2015,7(2):49.
[17] 樊丽颖,张佳宁,曹丽萍,等.Banach空间的β算子[J].哈尔滨理工大学学报,2018(2):140.
[18] ZHANG X.Fixed Point Theorem of Generalized Operator Quasi-contractive Mapping in Cone Metric Space[J].Afrika Matematika,2014,25(1):135.
[19] ZHANG X.Fixed Point Theorem of Generalized Operator Quasi-contractive Mapping in Cone Metric Space[J].Afrika Matematika,2014,25(1):135.
[20] 刘红玉.Banach不动点定理的推广及应用[J].广东石油化工学院学报,2015(3):75.
[21] PHUENGRATTANA W,SUANTAI S.Common Fixed Points of an Infinite Family of Nonexpansive mappings in Uniformly Convex Metric Spaces[J].Mathematical & Computer Modelling,2013,57(3/4):306.