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Banach空间中含A-单调映射的一类变分包含组 被引量：2

A New System of Variational Inclusions with A-monotone Mapping in Banach Spaces
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摘要 在一致光滑Banach空间,引入和研究了一类新的含A-单调映射的变分包含组问题.利用A-单调映射生成的邻近映射,给出了一类变分包含组问题的迭代算法,并证明了该迭代算法的收敛性,改进和推广了近期文献中的相关结果. In this paper,we introduce and study a new system of variational inclusions with A-monotone mapping in real smooth Banach spaces.By using the proximal mapping associated with the A-monotone operator,we construct a new iterative algorithm for solving this system of variational inclusions in real smooth Banach spaces.We also prove the existence of solutions for the system of variational inclusions and the convergence of iterative sequences generated by algorithm.Our results improve and generalize some known corresponding results.
作者 吴艳秋 王绍恒
机构地区 重庆三峡学院数学与计算机科学学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第5期614-616,共3页 Journal of Sichuan Normal University（Natural Science）
基金 重庆市科技攻关计划(2005EA7029)资助项目 重庆三峡学院科研项目(2007-252)的资助
关键词 A-单调映射 邻近映射 变分包含组 迭代算法 BANACH空间 A-monotone mapping proximal mapping system of variational inclusions iterative algorithm Banach spaces
分类号 O117.91 [理学—基础数学]
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参考文献12

  • 1Verma R U.Generalized nonlinear variational inclusion problems involving A-monotone mappings[J].Appl Math Lett,2006,19:960-963.
  • 2Zhang Q B.Generalized implicit variational-like inclusion problems involving G-η-monotone mappings[J].Appl Math Lett,2007,20(2):216-221.
  • 3Lan H Y,Cho Y J,Verma R U.Nonlinear relaxed cocoercive variational inclusions involving (A,η)-accretive mappings in Banach spaces[J].Comput Math Appl,2006,51:1529-1538.
  • 4Lan H Y.(A,η)-accretive mappings and set-valued variational inclusions with relaxed cocoercive mappings in Banach spaces[J].Appl Math Lett,2007,20(5):571-577.
  • 5Fang Y P,Huang N J,Thompson H B.A new system of variational inclusions with (H,η)-monotone operators in Hilbert spaces[J].Comput Math Appl,2005,49:365-374.
  • 6Fang Y P,Huang N J.H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces[J].Appl Math Lett,2004,17:647-653.
  • 7Ding X P,Xia F Q.A new class of completely generalized quasi-variational inclusions in Banach spaces[J].J Comput Appl Math,2002,147:369-383.
  • 8Xia F Q,Huang N J.Variational inclusions with a general H-monotone operator in Banach spaces[J].Comput Math Appl,2007,54:24-30.
  • 9Feng H R,Ding X P.A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces[J].J Comput Appl Math,2009,225(2):365-373.
  • 10Kazmi K R,Bhat M I.Iterative algorithm for a system of nonlinear variational-like inclusions[J].Comput Math Appl,2004,48:1929-1935.

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四川师范大学学报（自然科学版）
2010年 第5期

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