渐近非扩张型映像不动点的粘性逼近法*
2015-12-05李柳红王元恒
李柳红, 王元恒
(浙江师范大学数理与信息工程学院,浙江金华 321004)
渐近非扩张型映像不动点的粘性逼近法*
李柳红, 王元恒
(浙江师范大学数理与信息工程学院,浙江金华 321004)
在一致凸Banach空间E的非空闭凸子集C上研究了渐近非扩张映像T不动点问题,引入了一种新的更加广泛的粘性逼近迭代算法,在适当条件下证明了该迭代序列{xn}强收敛于映像T的不动点x*∈F(T),并且x*是一个变分不等式的解.所得结果改进和推广了其他相应结果.
粘性逼近;渐近非扩张映像;不动点;变分不等式;强收敛
0 引言
1 预备知识
2 主要结果
[1]Moudafi A.Viscosity approximation methods for fixed-points problems[J].J Math Anal Appl,2000,241(1):46-55.
[2]Xu Hongkun.Viscosity approximation methods for nonexpansive mappings[J].J Math Anal Appl,2004,298(1):279-291.
[3]王元恒,徐卫.非扩张映像不动点的一种变形迭代算法[J].浙江大学学报:理学版,2009,36(3):259-263.
[4]Goebel K,Kirk W A.A fixed point theorem for asymptotically nonexpansive mappings[J].Proc Am Math Soc,1972,35:171-174.
[5]曾六川.Banach空间中带误差的修正的Ishicawa迭代程序[J].数学学报,2004,47(2):219-228.
[6]Chen Junmin,Zhang Junmin,Fan Tiegang.Viscosity approximation methods for nonexpansive mappings and monotone mappings[J].J Math Anal Appl,2007,334(2):1450-1461.
[7]Song Yisheng,Chen Rudong,Zhou Haiyun.Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces[J].Nonlinear Anal,2007,66(5):1016-1024.
[8]赵良才,张石生.Banach空间中渐近非扩张映像具误差的强收敛性定理[J].数学学报,2008,51(1):99-108.
[9]董家帅,王元恒,罗红平.渐近非扩张型映像的黏性三步迭代序列强收敛性[J].浙江师范大学学报:自然科学版,2012,35(3):241-245.
[10]Ceng L C,Guu S M,Yao J C.A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces[J].Comput Math Appl,2011,61(9):2447-2455.
[11]罗红平,王元恒.三重复合修正的Ishikawa迭代序列强收敛性[J].浙江师范大学学报:自然科学版,2013,36(1):31-36.
[12]石惠敏,王元恒.渐近伪压缩映像不动点的三步带误差修正迭代逼近[J].系统科学与数学,2014,34(1):119-128.
[13]Wang Yuanheng,Xia Yonghui.Strong convergence of asymptotically pseudocontractions with the demiclosedness principle in Banach spaces[J].Fixed Point Theory Appl,2012,45:1-8.
[14]Cho Y J,Zhou Haiyun,Guo Ginti.Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings[J].Comput Math Appl,2004,47(4/5):707-717.
[15]Wang Yuanheng.Strong convergence theorems for asymptotically weak G-pseudo-ψ-contractive nonself-mappings with the generalized projection in Banach spaces[J].Abstr Appl Anal,2012,2012:1-11.
(责任编辑 陶立方)
A new viscosity approximating method for the fixed points of asymptotically nonexpansive mappings
LI Liuhong, WANG Yuanheng
(College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua Zhejiang 321004,China)
A new viscosity approximating method was introduced for the fixed points of an asymptotically nonexpansive mapping T in a nonempty closed convex subset C of an uniformly convex Banach space E.Under certain appropriate conditions,it was proved that the new iterative sequence{xn}converges strongly to a fixed point x*∈ F(T),which would be also the solution of a variational inequality.The results improved and extended the corresponding results reported by some other authors.
viscosity approximating method;asymptotically nonexpansive mapping;fixed point;variational inequality;strong convergence
O177.91
A
1001-5051(2015)01-0041-06
�:2014-06-18;
2014-09-22
国家自然科学基金资助项目(11271330);浙江省自然科学基金资助项目(LY14A010011)
李柳红(1988-),女,江西乐平人,硕士研究生.研究方向:非线性泛函分析.
王元恒.E-mail:yhwang@zjnu.cn
10.16218/j.issn.1001-5051.2015.01.007