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- 2018
分层混合均衡问题和不动点问题的等价性
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Abstract:
在Hilbert空间中,介绍了一类改进的混合均衡问题,并在适当条件下研究了混合均衡问题与不动点问题的等价关系,进一步建立了关于分层混合均衡问题解的一个充分必要条件.
In this paper, a class of modified mixed equilibrium problems is introduced in Hilbert space. The equivalence relation between the mixed equilibrium problems and a fixed point problem is studied under some suitable conditions. Moreover, a sufficient and necessary condition for the solution of modified split mixed equilibrium problems is established
[1] | JEONG J U. Generalized Viscosity Approximation Methods for Mixed Equilibrium Problems and Fixed Point Problems[J]. Appl Math Comput, 2016, 283: 168-180. |
[2] | KAZMI K R, REHAN A, MOHD F. Krasnoselski-Mann Type Iterative Method for Hierarchical Fixed Point Problem and Split Mixed Equilibrium Problem[J]. Numer Algor, 2017(4): 1-20. |
[3] | 闻道君. 广义平衡问题和渐近严格伪压缩映象的粘滞-投影方法[J]. 系统科学与数学, 2014, 34(6): 693-702. |
[4] | KAZMI K R, RIZVI S H. A Hybrid Extragradient Method for Approximating the Common Solutions of a Variational Inequality, a System of Variational Lnequalities, a Mixed Equilibrium Problem and a Fixed Point Problem[J]. Appl Math Comput, 2012, 218(2): 5439-5452. |
[5] | KONNOV I V, VOLOTSKAYA E O. Mixed Variational Inequalities and Economics Equilibrium Problems[J]. J Appl Math, 2002, 2(6): 289-314. DOI:10.1155/S1110757X02106012 |
[6] | KHUANGSATUNG W, KANGTUNYAKARN A. Algorithm of a New Variational Inclusion Problem and Strictly Pseudononspreading Mapping with Application[J]. Fixed Point Theory Appl, 2014(1): 1-27. |
[7] | TANG G, ZHU M, LIU H. A New Extragradient-Type Method for Mixed Variational Inequalities[J]. Operations Research Letters, 2015, 43(6): 567-572. DOI:10.1016/j.orl.2015.08.009 |
[8] | 徐洁, 张俊容, 刘佳. 求解一类广义均衡问题的交替方向法[J]. 西南大学学报(自然科学版), 2016, 38(5): 114-118. |
[9] | 闻道君. 关于伪单调平衡问题和不动点问题的粘滞-次梯度方法[J]. 数学进展, 2017, 46(2): 303-312. |
[10] | CROMBEZ G. A Hierarchical Presentation of Operators with Fixed Points on Hilbert Spaces[J]. Numer Funct Anal Optim, 2006, 27(3-4): 259-277. DOI:10.1080/01630560600569957 |