随机强伪压缩算子多步迭代序列的收敛性  

Convergence of multistep iterative sequences for random strongly pseudo-contractive operators

作　　者：聂辉 张树义[1] NIE Hui;ZHANG Shuyi(College of Mathematics and Physics,Bohai University,Jinzhou 121013,Liaoning Province,China)

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《天津师范大学学报（自然科学版）》2020年第4期14-19,共6页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11371070)。

摘　　要：在不设定任何有界性的条件下,在可分Banach空间中研究一类随机强伪压缩算子随机不动点的多步随机迭代序列的逼近问题,在适当的条件下建立了随机强伪压缩算子随机不动点的多步随机迭代序列的强收敛性定理.作为应用,建立了随机强增生算子方程随机解的Ishikawa迭代序列的强收敛性定理.通过算例验证了结论的有效性.所得结论改进和推广了相关文献中的结果.The multistep random iterative sequence approximation problem of random fixed points for a class of random strong-ly pseudo-contractive operators in separable Banach spaces is studied without any boundedness.Under suitable conditions,the strong convergence theorem of multistep random iterative sequences for random fixed points of random strongly pseudo-con-tractive operators is established.As an application,the strong convergence theorem of Ishikawa iterative sequence for random solutions of random strongly accretive operator equations is also established.An example is given to illustrate the validity of the results.The obtained conclusions extend and improve the corresponding results of some reference.

关 键 词：可测函数 随机强伪压缩算子 随机不动点 多步随机迭代序列 

分 类 号：O177.91[理学—数学]