非扩张映射的三步隐式双中点法则算法  

Three-step implicit double midpoint rule algorithm for non-expansive mapping

作　　者：高兴慧[1] 彭剑英 田迅杰 李苗苗 张玉婷 GAO Xinghui;PENG Jianying;TIAN Xunjie;LI Miaomiao;ZHANG Yuting(School of Mathematics and Computer Science,Yan’an University,Yan’an 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：《西南民族大学学报(自然科学版)》2025年第1期100-108,共9页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(61866038);省级大学生创新训练计划项目(S202410719077);延安大学十四五中长期重大科研项目(2021ZCQ012)。

摘　　要：不动点的迭代算法是非线性泛函分析研究的热点问题,在实一致光滑的Banach空间中介绍了三个非扩张映射的三步隐式双中点法则的新的迭代算法,在适当的假设条件下,用对偶映射的定义和Banach极限定义与技巧证明了算法所生成的序列强收敛于三个非扩张映射的不动点集与凸优化问题的公共元,其结果改进和推广了近期文献的相关结果.The iterative algorithm for fixed points is a hot problem in the study of nonlinear functional analysis.In the real uniform and smooth Banach space,a new iterative algorithm of the three-step implicit double midpoint rule of three non-expansion mappings was introduced.Under appropriate assumptions,the definition of dual mappings and Banach limit definitions and techniques were used to prove that the sequence generated by the algorithm strongly converged to the fixed point set of three non-expansion mappings and the common element of the convex optimization problem.The results improved and generalized the relevant results in recent literature.

关 键 词：三步隐式双中点法则 强收敛 非扩张映射 BANACH空间 

分 类 号：O177.91[理学—数学]