(α,β)-广义混合集值映射的吸收点和收敛性定理  

Attractive Points and Convergence Theorems of ( α,β)-Generalized Hybrid Set-valued Mappings

作　　者：陈丽丽 邹洁 高璐 CHEN Li-li;ZOU Jie;GAO Lu(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院

出　　处：《哈尔滨理工大学学报》2019年第3期138-142,共5页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11401141);黑龙江省博士后科研资助项目(LBH-Z15098)

摘　　要：集值映射理论在控制论、优化理论、数理经济等诸多领域都有着广泛的应用,现已成为非线性分析的重要组成部分,因此研究集值映射的有关问题具有重要的理论意义和应用价值。主要研究了一致凸的Banach空间上(α,β)-广义混合集值映射吸收点的收敛性问题,引入了集值映射意义下的Agarwal迭代格式,并分别利用I’条件和半紧性质给出了一致凸的Banach空间上(α,β)-广义混合集值映射在该迭代格式下关于吸收点的收敛性定理。Set-valued mapping theory,which is widely used in control theory,optimization theory,mathematical economics and other fields,has developed rapidly in recent decades and has now become an important component of nonlinear analysis.Therefore,research on related problems of set value mappings has an important theoretical significance and application value.We mainly discuss the convergence problems of attractive points of(α,β)-generalized hybrid set-valued mappings,and we also generalize the Agarwal iteration to the case of set-valued mappings.Consequently,some convergence theorems of attractive points of(α,β)-generalized hybrid set-valued mappings defined on uniformly convex Banach spaces by use of the conditions I′and the demi-compact property are obtained respectively.

关 键 词：Agarwal迭代格式 (α β)-广义混合集值映射 吸收点 一致凸Bananch空间 

分 类 号：O177[理学—数学]