非扩张映射的广义粘性三步隐式双中点法则  

Generalized Viscosity Three-step Implicit Double Midpoint Rule for Non-expansive Mappings

作　　者：彭剑英 高兴慧[1] 张玉婷 PENG Jianying;GAO Xinghui;ZHANG Yuting(School 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：《广西师范大学学报（自然科学版）》2024年第6期194-204,共11页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(61866038);延安大学科研计划项目(2023JBZR-012);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,本文在实一致光滑Banach空间中构造新的非扩张映射不动点的广义三步隐式双中点法则的粘性算法,在适当条件下,用对偶映射和Banach极限的定义与技巧,证明由该算法生成的迭代序列强收敛于3个非扩张映射的公共不动点集的公共元,给出其特殊情况下的推论。本文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 topic in nonlinear functional analysis research.The viscosity algorithm for constructing a new generalized three-step implicit double midpoint rule for non-expanding mappings with fixed points in a uniformly smooth Banach spaces is proposed.Under appropriate conditions,the dual mapping definition and Banach limit definition and techniques are used to prove that the iterative sequence generated by this algorithm strongly converges to the common element of the common fixed point set of three non-expanding mappings,and the inference in special cases is given.The results improve and generalize the relevant results in recent literature.

关 键 词：BANACH空间 非扩张映射 广义隐式双中点法则 强收敛 不动点 

分 类 号：O177.91[理学—数学]