两个可数族严格伪压缩映射的分裂公共不动点迭代逼近算法  

A new iterative algorithm for the split common fixed points of two infinite countable families of the strictly pseudo-contractive mappings

作　　者：王元恒 章杰 WANG Yuanheng;ZHANG Jie(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华\321004

出　　处：《浙江师范大学学报（自然科学版）》2021年第1期1-8,共8页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11671365);浙江省自然科学基金资助项目(LY14A010011)。

摘　　要：为了进一步研究广义非线性算子分裂公共不动点这个热点问题,在Hilbert空间中利用加权平均迭代逼近方法,给出了2个关于严格伪压缩映射的特征性质,构建了一个新的对于2个可数族严格伪压缩映射的分裂公共不动点的迭代逼近序列,在较弱条件下证明了该序列的3个弱、强收敛性定理,作为应用,可求解一类可数族广义分裂等式问题.研究结果改进和推广了许多相关文献的近代结果.It was aimed to study the common split fixed point problem for generalized nonlinear operators in Hilbert spaces.Two characteristic properties of the strictly pseudo-contractive mappings were given and a new iterative algorithm for the split common fixed points of two infinite families of the strictly pseudo-contractive mappings was established by using the method of approximating iterative sequences.Under some certain weak conditions,three weak and strong convergence theorems were proved for the iterative sequences.As an application,a new kind of two infinite countable families generalized split equality problem was solved.Many corresponding results in other literatures were improved and generalized by the presented results.

关 键 词：严格伪压缩映射 分裂公共不动点 广义分裂等式 强弱收敛性 

分 类 号：O177.91[理学—数学]