关于Banach空间中三元集值拟压缩映射变分包含组问题  

On a System of Variational Inclusions Involving Triple Elemnet Set-valued Quasi-contractive Mappings in Banach Spaces

作　　者：赵梓汝 赵亚莉 王凯文 黄晓晴 ZHAO Zi-ru;ZHAO Ya-li;WANG Kai-wen;HUANG Xiao-qing(School of Mathematical Science,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《数学的实践与认识》2023年第8期222-236,共15页Mathematics in Practice and Theory

基　　金：辽宁省教育厅科学基金(LJKMZ20221491)。

摘　　要：在实Banach空间中提出并研究了一个新的涉及集值拟压缩、具有非空闭凸值的下半连续映射的三元变分包含组.首先,利用集值拟压缩映射不动点的存在性证明了集值变分包含组解的存在性.然后,利用集值变分包含组解的存在性,构造一个新的迭代算法并证明了由迭代算法生成的迭代序列的强收敛性.所得结果推广了已有的结论.In this paper,a new system of variational inclusions involving triple element set-valued quasi-contractive,lower semi-continuous mappings with nonempty closed convex values is introduced and studied in a real Banach spaces.First,the existence of the solution to the system of variational inclusions considered here is obtained by virtue of the existence and unique of the fixed point of a quasi-contractive mapping.Then,using the existence result,a new iterative algorithm is proposed and the strong convergence is proved.The results presented here improve and extend some known results.

关 键 词：集值变分包含组 拟压缩映射 不动点 迭代算法 强收敛性 

分 类 号：O177.2[理学—数学]