非扩张映射族和单调映射迭代算法的收敛性  

The Convergence of Iterative Methed for Families of Nonexpansive Mappings and Monotone Mappings

作　　者：史沧红[1] 吴定平[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2013年第1期72-77,共6页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(11171046);成都信息工程学院科研项目(KYTZ201004)资助

摘　　要：针对Yonghong Yao等给出的在Hilbert空间中单个非扩张映射和单调映射的迭代算法,和目前对非扩张映射族和其他映射之间迭代方法研究较少的前提下,结合Tomoo Shimizu等给出的在Hilbert空间中非扩张映射族的迭代算法,提出了非扩张映射族与α-逆-强单调映射的迭代算法。通过建立相应的收敛性定理,利用迭代算法,得到非扩张映射族公共不动点集和α-逆-强单调映射变分不等式解集的公共元。研究结果表明这个迭代序列强收敛于这一公共元。Based on the terative algorithm of a nonexpansive mapping and a monotone mapping in Hilbert spaces given by Yonghong Yao etc, under the situation that currently less iterative method between nonexpansive mapping fami- lies and other mappings are studied, integrating the iterative algorithm for families of nonexpansive mappings in Hilbert spaces given by Tomoo Shimizu etc, we introduce a new iterative scheme of nonexpansive families mappings and a-inverse-strongly monotone mappings. Through the establishment of a strong convergence theorem and by using the new iterative algorithm, we got the common element of the set of fixed points of families of nonexpansive map- pings and the set of solutions of the variational for a-inverse-strongly monotone mappings. The results show that the iterative scheme converges strongly to the common element.

关 键 词：基础数学 α逆-强单调映射 强收敛性 变分不等式 非扩张映射族 

分 类 号：O177.91[理学—数学]