弱相对非扩张映像不动点单调CQ算法与应用

Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications

中文关键词:  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.

英文关键词:weak relatively nonexpansive mapping  generalized projection  asymptotic fixed point  monotone $CQ$ method  maximal monotone operator.

中文摘要:

      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.

英文摘要:

      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.