(α,β)-广义混合集值映射的吸收点和收敛性定理

2019-07-31 05:05陈丽丽邹洁高璐
哈尔滨理工大学学报 2019年3期
关键词:收敛性广义定理

陈丽丽 邹洁 高璐

摘 要:集值映射理論在控制论、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。

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

DOI:10.15938/j.jhust.2019.03.023

中图分类号: O177.2

文献标志码: A

文章编号: 1007-2683(2019)03-0138-05

Abstract:Setvalued 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 setvalued mappings, and we also generalize the Agarwal iteration to the case of setvalued mappings. Consequently, some convergence theorems of attractive points of (α,β)-generalized hybrid setvalued mappings defined on uniformly convex Banach spaces by use of the conditions I′ and the demicompact property are obtained respectively.

Keywords:Agarwal iteration; (α,β)-generalized hybrid setvalued mapping; attractive point; uniformly convex Banach space

3 结 论

本文主要研究了(α,β)-广义混合集值映射在Agarwal迭代格式下的吸收点和收敛性问题, 事实上,Agarwal迭代速度在某些条件下比引言中2015年Y.C.Zheng给出的迭代格式收敛速度更快。 我们分别利用I′条件和半紧性质给出了一致凸Banach空间上(α,β)-广义混合集值映射的收敛定理,在此基础上可以继续研究(α,β)-广义混合集值映射及其它类型的广义集值映射的吸收点和收敛性问题。

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(編辑:关 毅)

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