一类Curvature方程组解的迭代逼近  

Iterative Approximation to Solution of One Kind Curvature Systems

作　　者：魏利[1] 师爱芬[1] 

机构地区：[1]河北经贸大学数学与统计学学院

出　　处：《应用数学》2015年第4期761-770,共10页Mathematica Applicata

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点项目(ZH2012080);河北经贸大学科研重点项目(2013KYZ01)

摘　　要：本文给出一类Curvature方程组解的构造,并建立其解与有限个极大单调算子公共零点之间的关系.借助于极大单调算子的广义豫解式,设计新的投影迭代算法,利用Lyapunov泛函、广义投影映射和保核收缩映射等工具,证明迭代序列在Banach空间中强收敛到有限个极大单调算子公共零点的结论.进而得到Curvature方程组解的迭代逼近序列.推广和补充了以往的相关研究成果.In this paper, the construction of the solution of one kind curvature systems is studied and the connection between this solution and the common zeros of finitely many maximal monotone operators is investigated. Some new iterative schemes are constructed in view of the generalized resolvent of maximal monotone operators. By using the techniques of Lyapunov functional, generalized projection mapping and retraction, etc, the iterative schemes are proved to be strongly convergent to common zeros of finitely many maximal monotone operators in Banach spaces and then iterative approximate sequences of the solution of the curvature systems are obtained, which extend and complement some previous corresponding work.

关 键 词：广义豫解式 保核收缩映射 LYAPUNOV泛函 极大单调算子 零点 Curvature方程组 

分 类 号：O177.91[理学—数学]