有限族广义一致伪Lipschitz映象公共不动点的迭代收敛性  

Iterative Convergence of Common Fixed Points for a Finite Family of Generalized Uniform Quasi-Lipschitz Mappings

作　　者：赵美娜[1] 张树义[1] 赵亚莉[1] 

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《烟台大学学报（自然科学与工程版）》2017年第1期7-10,60,共5页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11371070)

摘　　要：目的是在Banach空间中引入并研究一类广义一致伪Lipschitz映象,举例说明这种映象的广泛性,并在一定条件下,证明了一族广义一致伪Lipschitz映象公共不动点的带误差的多步迭代序列收敛的充分必要条件,从而改进与推广了一些已知的结果.获得的收敛准则丰富了非线性算子不动点的迭代逼近理论.The purpose of this paper is to introduce and study a new class of generalized uniform quasi-Lipschitz mappings in Banach spaces and give an example to illustrate the universality of this kind of mapping. The sufficient and necessary condition for the multi-step iterative sequences with errors to converge strongly to a common fixed point for a finite family of generalized uniform quasi-Lipschitz mappings is proved under certain conditions, which improve and extend some recent results. We obtain the convergence criterion to enrich the iterative approximation theory of fixed point for nonlinear operators.

关 键 词：一致伪Lipschitz映象 广义一致伪Lipschitz映象 公共不动点 多步迭代序列 

分 类 号：O177.91[理学—数学]