自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

丁协平

doi:10.3879/j.issn.1000-0887.2011.02.010

自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

doi: 10.3879/j.issn.1000-0887.2011.02.010

丁协平

四川师范大学数学与软件科学学院,成都 610068

基金项目: 四川省重点学科建设基金资助项目(SZD0406);四川师范大学重点科研基金(09ZDL04)资助

详细信息

作者简介:
丁协平(1938- ),男,四川自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

中图分类号: O177.91;O178;O241.7
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- 文章访问数: 1684
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出版历程
- 收稿日期: 2010-09-16
- 修回日期: 2010-01-05
- 刊出日期: 2011-02-15

Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

DING Xie-ping

College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P. R. China

摘要

摘要: 在自反Banach空间内引入和研究了一类新的涉及广义混合似变分不等式问题的广义混合平衡问题组(SGMEP)．首先,为了求解 SGMEP,引入了一类辅助广义混合平衡问题组(SAGMEP)．在没有任何强制条件的相当温和假设下, 对SAGMEP证明了解的存在性和唯一性．其次, 利用辅助原理技巧,对求解SGMEP建议和分析了一类新的迭代算法．最后,在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性．这些结果改进、统一和推广了这一领域内某些最近结果．
- 广义混合隐平衡问题组 /
- 辅助原理 /
- 迭代算法 /
- 自反Banach空间
Abstract: A system of new generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems (SGMEP) was introduced and studied in reflexive Banach spaces. First,a system of auxiliary generalized mixed equilibrium problems (SAGMEP) for solving the SGMEP was introduced. The existence and uniqueness of the solutions of the SAGMEP was proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Next,by using the auxiliary principle technique,a new iterative algorithm for solving the SGMEP was suggested and analyzed. Finally,the strong convergence of the iterative sequences generated by the algorithm was also proved under quite mild assumptions without any coercive conditions. These results improve,unify and generalize some recent results in this field.
- system of generalized mixed equilibrium problems /
- auxiliary principle /
- iterative algorithm /
- reflexive Banach space

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参考文献(16)

[1]	Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems[J].Math Students, 1994, 63(1): 123-145.
[2]	Moudafi A, Théra M. Proximal and Dynamical Approaches to Equilibrium Problems[M].Lecture Notes in Economics and Mathematical Systems. Vol 477. Berlin: Springer-Verlag, 1999: 187-201.
[3]	Moudafi A. Mixed equilibrium problems: sensitivity analysis and algorithmic aspects[J]. Comput Math Appl, 2002, 44(8/9): 1099-1108. doi: 10.1016/S0898-1221(02)00218-3
[4]	DING Xie-ping. Existence and algorithm of solutions for nonlinear mixed quasi-variational inequalities in Banach spaces[J].J Comput Appl Math, 2003, 157(2): 419-434. doi: 10.1016/S0377-0427(03)00421-7
[5]	DING Xie-ping. Iterative algorithm of solutions for generalized mixed implicit equilibrium-like problems[J]. Appl Math Comput, 2005, 162(2): 799-809. doi: 10.1016/j.amc.2003.12.127
[6]	Ding X P. Existence of solutions and an algorithm for mixed variational-like inequalities in Banach spaces[J]. J Optim Theory Appl, 2005, 127(2): 285-302. doi: 10.1007/s10957-005-6540-y
[7]	DING Xie-ping, YAO Jen-chin. Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces[J]. Comput Math Appl, 2005, 49(5/6): 857-869. doi: 10.1016/j.camwa.2004.05.013
[8]	Kazmi K R, Khan F A. Existence and iterative approximation of solutions of generalized mixed equilibrium problems[J]. Comput Math Appl, 2008, 56(5): 1314-1321. doi: 10.1016/j.camwa.2007.11.051
[9]	丁协平, 王中宝. Banach空间内涉及H-η-单调算子的集值混合拟似变分包含组[J]. 应用数学和力学, 2009, 30(1):1-14.(DING Xie-ping，WANG Zhong-bao. System of set-valued mixed quasi-variational-like inclusions involving H-eta-monotone operators in Banach Spaces[J]. Applied Mathematics and Mechanics(English Edition), 2009, 30(1):1-12.)
[10]	丁协平. Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法[J]. 应用数学和力学, 2010, 31(9): 1001-1015.(DING Xie-ping. Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(9): 1049-1062.)
[11]	DING Xie-ping, WANG Zhong-bao. The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces[J]. J Comput Appl Math, 2010, 223(11): 2876-2883.
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[14]	DING Xie-ping, Tan Kok-keong. A minimax inequality with applications to existence of equilibrium point and fixed point theorems[J]. Colloq Math, 1992, 63: 233-247.
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[16]	Pascall D, Sburlan S. Nonlinear Mappings of Monotone Type[M].Alphen aan den Rijn, Netherlands: Sijthoff and Noordhoff International Publishers, 1978.

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自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

doi: 10.3879/j.issn.1000-0887.2011.02.010

作者简介:
丁协平(1938- ),男,四川自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

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Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

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自反Banach空间内一类新的广义混合平衡问题组的辅助原理和逼近可解性

doi: 10.3879/j.issn.1000-0887.2011.02.010

作者简介: 丁协平(1938- ),男,四川自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

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Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

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出版历程

目录

作者简介:
丁协平(1938- ),男,四川自贡人,教授(联系人.Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).