余强制映射的广义半闭性原理及应用  

Generalized semi-closedness principle for coercive mappings and its applications

作　　者：曾炫淇 罗馨缘 冯世强[1] ZENG Xuanqi;LUO Xinyuan;FENG Shiqiang(School of Mathematic and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《内江师范学院学报》2022年第10期36-40,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(11871059);四川省高校创新团队项目(16TD0019)。

摘　　要：半闭性原理是研究迭代方法收敛性的有力工具.为了提供这个原理的扩展,将余强制映射的半闭性原理推广到了更广的空间并改进了收敛条件,使其适用范围更广.应用推广后的原理,进一步得到了稳定非扩张映射的广义半闭性原理和平衡余强制映射的广义半闭性原理.Semi-closedness principle is a powerful tool in the study of convergence of iterative methods.In order to provide extensions of this principle,the principle for coercive mappings is extended to a wider space,and the convergence conditions are improved to enlarge its applicability.By applying the generalized principle,the generalized semi-closedness principle for firmly non-expansive mappings and semi-closedness principle for balanced coercive mappings are both obtained.

关 键 词：半闭性原理 余强制映射 稳定非扩张映射 弱收敛 加权内积 

分 类 号：O224[理学—运筹学与控制论]