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弱相对非扩张映像不动点单调CQ算法与应用
引用本文:苏永福,高俊宇,周海云.弱相对非扩张映像不动点单调CQ算法与应用[J].数学研究与评论,2008,28(4):957-967.
作者姓名:苏永福  高俊宇  周海云
作者单位:天津工业大学理学院数学系, 天津 300160;沧州师范专科学校数学系, 河北 沧州 300160;石家庄军械工程学院数学系, 河北 石家庄 050003
基金项目:国家自然科学基金(No.10771050).
摘    要:Kamimura和Takahashi$^{7]}$证明了相对非扩张映像CQ迭代算法的强收敛定理.该文构造了单调CQ算法, 用来逼近弱相对非扩张映像不动点, 证明了强收敛定理. 并将结果应用于逼近Banach空间极大单调算子的零点. 单调CQ算法比目前的CQ算法收敛速度快. 另外, 为证明弱相对非扩张映像不动点强收敛定理,该文运用了新的Cauchy列证明方法, 而不用Kadec-Klee性质, 该文结果改进了S.Matsushita 和 W.Takahashi及其它人的结果.

关 键 词:弱相对非扩张映像    广义投影    渐近不动点    单调CQ算法    极大单调算子.
收稿时间:2006/9/22 0:00:00
修稿时间:2007/3/23 0:00:00

Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications
SU Yong Fu,GAO Jun Yu and ZHOU Hai Yun.Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications[J].Journal of Mathematical Research and Exposition,2008,28(4):957-967.
Authors:SU Yong Fu  GAO Jun Yu and ZHOU Hai Yun
Institution:Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;Department of Mathematics, Cangzhou Normal College, Hebei 061001, China;Department of Mathematics, Shijiazhuang Mechanical Engineering College, Hebei 050003, China
Abstract:Matsushita, Takahashi$^{4]}$ proved a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method ($CQ$ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Takahashi by monotone $CQ$ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone $CQ$ method is faster than the hybrid method of Matsushita, Takahashi. In addition, the Cauchy sequence method is used in this paper without using the Kadec-Klee property. The results of this paper modify and improve the results of Matsushita, Takahashi and some others.
Keywords:weak relatively nonexpansive mapping  generalized projection  asymptotic fixed point  monotone $CQ$ method  maximal monotone operator  
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