A NEW HYBRID-EXTRAGRADIENT METHOD FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS
A NEW HYBRID-EXTRAGRADIENT METHOD FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS
复制标题
DOI：
10.11650/twjm/1500405033
复制
发表时间：
2008-01
影响因子：
0.4
通讯作者：
Jian-Wen Peng;J. Yao
中科院分区：
文献类型：
--
作者：
Jian-Wen Peng;J. Yao
本文引入了一种新的基于混合方法和超梯度方法的迭代格式，用于寻找广义混合平衡问题的解集、非扩张映象的不动点集和单调Lipschitz连续映象的变分不等式集的公共元素.在Hilbert空间中，我们得到了由这些过程生成的序列的一个强收敛定理。在此基础上，我们还得到了一些新的有趣的结果.本文的结果推广、推广和统一了文献中一些著名的强收敛定理。
In this paper, we introduce a new iterative scheme based on the hybrid method and the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of the variational inequality for a monotone, Lipschitz-continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend and unify some well-known strong convergence theorems in the literature.