Wang Qian-Wen, Guan Jin-Lin, Ceng Lu-Chuan, Hu Bing
1Department of Mathematics, Shanghai Normal University, Shanghai, China.
2LAMPS and Department of Mathematics and Statistics, York University, Toronto, Canada.
J Inequal Appl. 2018;2018(1):315. doi: 10.1186/s13660-018-1899-0. Epub 2018 Nov 16.
In this paper, we introduce two general iterative methods (one implicit method and one explicit method) for finding a solution of a general system of variational inequalities (GSVI) with the constraints of finitely many generalized mixed equilibrium problems and a fixed point problem of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed implicit and explicit iterative methods to a solution of the GSVI with the above constraints, which is the unique solution of a certain variational inequality. The results presented in this paper improve, extend, and develop the corresponding results in the earlier and recent literature.
在本文中，我们引入了两种通用的迭代方法（一种隐式方法和一种显式方法），用于在希尔伯特空间中求解具有有限多个广义混合平衡问题约束和连续伪压缩映射不动点问题的广义变分不等式系统（GSVI）。然后，我们建立了所提出的隐式和显式迭代方法到具有上述约束的GSVI解的强收敛性，该解是某个变分不等式的唯一解。本文给出的结果改进、扩展并发展了早期和近期文献中的相应结果。
