摘要
在实一致凸且q一致光滑Banach空间中,利用Sunny保核收缩映射,构造了一种新的迭代格式.借助于Lyapunov泛函,度规函数与广义投影映射等分析工具,证明了迭代序列{x_n}强收敛到无穷个m增生映射{Ai}与无穷个θ_i逆强增生映射{B_i}之和的公共零点的结论.进行了数值试验验证了迭代格式的合理性.将以往在Hilbert空间中的相关研究成果推广到了较一般的Banach空间中.最后,展示了新迭代算法在微分边值系统,凸规划问题和极大极小问题上的应用.
In this paper,a new iterative scheme is constructed in a real uniformly convex and q-uniformly smooth Banach space by using Sunny retraction.It is proved that the iterative sequence fxng converges strongly to the common zero point of the sum of infinite m-accretive mappings(Ai}and infiniteμi-inversely strongly accretive mappings{Bi},where Lyapunov functional,gauge function and generalized projection mapping are employed as analyzing tools.Some numerical experiments are conducted to verify the effectiveness of the iterative scheme.The conclusions extend some corresponding results from Hilbert space to a more general Banach space.Finally,the applications of the new iterative scheme to differential boundary systems,convex program and minimax problems are exemplified.
作者
魏利
申延伟
郑亚勤
WEI Li;SHEN Yan-wei;ZHENG Ya-qin(School of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,China;College of Science,Agricultural University of Hebei,Baoding 071001,China)
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2018年第4期477-488,共12页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11071053)
河北省自然科学基金(A2014207010)
河北省教育厅科研重大项目(ZD2016024)
河北省教育厅科学研究计划项目青年基金(QN2017328)
河北经贸大学科研重点项目(2016KYZ07)
河北农业大学理工基金(LG201612)
