Fixed point solutions of generalized equilibrium problems for nonexpansive mappings
Fixed point solutions of generalized equilibrium problems for nonexpansive mappings
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DOI：
10.1016/j.cam.2010.01.055
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
Y. Shehu
中科院分区：
文献类型：
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作者：
Y. Shehu
在本文中，我们介绍了一种迭代方案，用于查找实希尔伯特空间中非扩张映射的不动点集和广义平衡问题的解集的公共元素。然后，证明了该方案对两个集合的公共元素的强收敛性。作为一个应用，解决了寻找非扩张映射的不动点集合和平衡问题的解集合的公共元素的问题。此外，还给出了寻找非扩张映射不动点集和变分不等式问题的解集的公共元素问题的解决方案。
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a generalized equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved. As an application, problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem is solved. Moreover, solution is given to the problem of finding a common element of fixed points set of nonexpansive mappings and the set of solutions of a variational inequality problem.