g-Eta-单调映像和解广义隐似变分包含的预解算子技巧

张清邦; 丁协平

g-Eta-单调映像和解广义隐似变分包含的预解算子技巧

张清邦^1,2,
丁协平²

1.
北京工业大学应用数理学院,北京 100022;2.四川师范大学数学与软件科学学院,成都 610066

基金项目: 四川省教育厅重点科研基金资助项目(2003A081)

详细信息

作者简介:
张清邦(1972- ),男,四川南江人,博士(联系人.E-mail:q.b.zhang@emails.bjut.edu.cn).

中图分类号: O177.91
计量
- 文章访问数: 2523
- HTML全文浏览量: 100
- PDF下载量: 661
- 被引次数: 0
出版历程
- 收稿日期: 2003-12-17
- 修回日期: 2006-10-11
- 刊出日期: 2007-01-15

g-Eta-Monotone Mapping and Resolvent Operator Technique for Solving Generalized Implicit Variational-Like Inclusions

ZHANG Qing-bang^1,2,
DING Xie-ping²

1.
College of Applied Sciences, Beijing University of Technology, Beijing 100022, P. R. China;

摘要

摘要: 引入一类新的g-Eta-单调映像和一类涉及g-Eta-单调映像的广义隐似变分包含；定义了g-Eta-单调映像的预解算子，并证明了其Lipschitz连续性；分析和给出了这类涉及g-Eta-单调映像的广义隐似变分包含的迭代算法，并证明了其收敛性．
- g-η-单调映像 /
- 预解算子 /
- 广义隐似变分包含 /
- 迭代算法
Abstract: A new class of g-Eta-monotone mappings and a class of generalized implicit variational-like inclusions involving g-Eta-monotone mappings are introduced. The resolvent operator of g-Eta-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequence generated by the algorithm is also proved.
- g-η-monotone mapping /
- resolvent operator /
- generalized implicit variational-like inclusion /
- iterative algorithm

HTML全文

参考文献(14)

[1]	Noor M A. Generalized set-valued variational inclusions and resolvent equations[J].J Math Anal Appl,1998,228(1):206-220. doi: 10.1006/jmaa.1998.6127
[2]	DING Xie-ping. Generalized implicit quasivariational inclusions with fuzzy set-valued mapping[J].Comput Math Applic,1999,38(1):71-79.
[3]	DING Xie-ping. Generalized quasi-variational-like inclusions with fuzzy mapping and nonconvex functionals[J].Adv Nonlinear Var Inequal,1999,2(2):13-29.
[4]	DING Xie-ping,Park J Y.A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mapping[J].J Comput Appl Math,2002,138(2):243-257. doi: 10.1016/S0377-0427(01)00379-X
[5]	DING Xie-ping.Algorithms of solutions for completely generalized mixed implicit quasi-variational inclusions[J].Appl Math Comput,2004,148(1):47-66. doi: 10.1016/S0096-3003(02)00825-1
[6]	Liu L W,Li Y Q.On generalized set-valued variational inclusions[J].J Math Anal Appl,2001,261(1):231-240. doi: 10.1006/jmaa.2001.7493
[7]	FANG Ya-ping,HUANG Nan-jing.H-monotone operator and resolvent operator technique for variational inclusions[J].Appl Math Comput,2003,145(2/3):795-803. doi: 10.1016/S0096-3003(03)00275-3
[8]	Lee C H, Ansari Q H, Yao J C. Aperturbed algorithms for strongly nonlinear variational-like inclusion[J].Bull Austral Math Soc,2000,62(3):417-426. doi: 10.1017/S0004972700018931
[9]	DING Xie-ping.Generalized quasi-variational-like inclusions with nonconvex functionals[J].Appl Math Comput,2001,122(3):267-282. doi: 10.1016/S0096-3003(00)00027-8
[10]	Noor M A. Nonconvex functions and variational inequalities[J].J Optim Theory Appl,1995,87(3):615-630. doi: 10.1007/BF02192137
[11]	DING Xie-ping,LOU Chung-lin.Perturbed proximal point algorithms for general quasi-variational-like inclusions[J].J Comput Appl Math,2000,113(1/2):153-165. doi: 10.1016/S0377-0427(99)00250-2
[12]	HUANG Nan-jing,FANG Ya-ping.A new class of general variational inclusions involving maximal η-monotone mappings[J].Publ Math Debrecen,2003,62(1/2):83-98.
[13]	DING Xie-ping.Predictor-corrector iterative algorithms for solving generalized mixed variational-like inequalities[J].Appl Math Comput,2004,152(3):855-865. doi: 10.1016/S0096-3003(03)00602-7
[14]	Nadler S B. Mutivalued contraction mapping[J].Pacific J Math,1969,30(3):457-488.