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Banach空间中一类变分包含组的Mann迭代算法(英文) 被引量：6

Mann Iterative Algorithm for a System of Variational Inclusions in Banach Spaces
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摘要 在Banach空间中引入和研究了一类含(A,η)-增生映象的变分包含,利用与(A,η))-增生映象相联系的预解算子性质,证明了这类变分包含解的存在性和唯一性.对这类变分包含的逼近解也建立了一个新的Mann迭代算法,并讨论了算法的收敛性. In this paper, we introduce and study a system of variational inclusions involving （A, η） -accretive mappings in Banach spaces. Using the resolvent operator associated with （A, η） -accretive mappings, we prove the existence and uniqueness of the solution for this system of variational inclusions. We also construct a new Mann iterative algorithm for approximating the solution of this system of variational inclusions and discuss the convergence of the algorithm.
作者 金茂明 廖正琦
机构地区 后勤工程学院 重庆交通大学理学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第12期12-15,共4页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(10471151) 重庆市教委科技资助项目(KJ071305).
关键词 (A η)-增生映象 松驰余强制映象 变分包含组 预解算子 存在性和收敛性 （A, η）-accretive mapping relaxed cocoercive mapping system of variational inclusion resolvent operator existence and convergence
分类号 O177.91 [理学—基础数学]
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参考文献10

  • 1[1]Ding X P,Luo C L.Perturbed Proximal Point Algorithms for Generalized Quasi-Variational-Like Inclusions[J].J Comput Appl Math,2000,210:153-165.
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同被引文献38

  • 1王绍荣,杨泽恒.Banach空间中的渐近拟非扩张型映象不动点的具混合误差的Ishikawa迭代逼近问题[J].西南师范大学学报（自然科学版）,2004,29(4):578-581. 被引量：9
  • 2王亚琴.Banach空间中有限族渐近非扩张映象的新隐迭代程序[J].贵州师范大学学报（自然科学版）,2004,22(4):60-63. 被引量：1
  • 3韦增欣,谢品杰,顾能柱.一类拟牛顿算法的收敛性[J].广西科学,2006,13(4):282-287. 被引量：7
  • 4[1]Jin M M.Iterative Algorithms for a New System of Nonlinear Variational inclusions with(A,η)-Accretive Mappings in Banaeh Spaces[J].Comput Math Appl,2007,54:579-588.
  • 5[3]Kim J K,Kim D S.A New System of Generalized Nonlinear Mixed Variational Inequalities in Hilbert Spaces[J].J Convex Anal,2004,11:235-243.
  • 6[4]Peng J W,Zhu D L.Existence of Solutions and Convergence of Iterative Algorithms for a System of Generalized Nonlinear Mixed Quasi-Variational Inclusions[J].Comput Math Appl,2007,53:693-705.
  • 7[5]Verma R U.Proiection Methods,Algorithms,and a New System of Nonlinear Variational Inequalities[J].Comput Math Appl,2001,41:1025-1031.
  • 8[6]Verma R U.General Convergence Analysis for Two-Step Projection Methods and Application to Variational Problems[J].Appl Math Lett,2005,18:1286-1292.
  • 9[7]Lan H Y,Cho Y J,Verma R U.On Nonlinear Relaxed Cocoercive Variational Inclusions Involving(A,η)-Accretive Mappings in Banach Spaces[J].Comput Math Appl,2006,51:1529-1538.
  • 10[8]Xu H K.Inequalities in Banach Spaces with Applications[J].Nonlinear Anal,1991,16(12):1127-1138.

引证文献6

二级引证文献5

西南大学学报（自然科学版）
2007年 第12期

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