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

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.