G-非扩张映射有限族的多步迭代方法及其数值实验  

A new multi-step iteration method and its numerical realization for a finite family of G-nonexpansive mappings

作　　者：高兴慧[1] 何纪元 任欣怡 杨大庆 赵海洋 樊子秋 贾倩倩 GAO Xinghui;HE Jiyuan;REN Xinyi;YANG Daqing;ZHAO Haiyang;FAN Ziqiu;JIA Qianqian(College of Mathematics and Computer Science,Yan'an University,Yan'an,Shaanxi 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州师范大学学报（自然科学版）》2022年第6期17-22,共6页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(61866038);延安大学科研计划项目(YDY2019-15);2020年陕西省大学生创新训练计划项目(S202010719077)。

摘　　要：在带有有向图的一致凸的Banach空间中,构造了一种关于G-非扩张映射有限族的公共不动点的多步迭代方法,并利用所构造的迭代方法证明了G-非扩张映射有限族的强、弱收敛定理,最后给出数值例子验证所提出的迭代方法的有效性。In a uniformly convex Banach space with a directed graph,a new multi-step iteration method is constructed to approximate the common fixed point of a finite family of G-nonexpansive mappings.The constructed iteration method is used to prove the strong and weak convergence theorems of the common fixed point.A numerical example is given to verify the advantages of this method.

关 键 词：G-非扩张映射有限族 多步迭代 强收敛定理 弱收敛定理 

分 类 号：O177.91[理学—数学]