Cheawchan Kanyarat, Kangtunyakarn Atid
Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand.
J Inequal Appl. 2018;2018(1):122. doi: 10.1186/s13660-018-1716-9. Epub 2018 May 22.
In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme for finding a common element of the set of solutions of variational inequality problems and the set of common fixed points of a finite family of quasi-nonexpansive mappings and the set of solutions of the modified split generalized equilibrium problem without assuming a demicloseness condition and , where is a quasi-nonexpansive mapping and ; a difficult proof in the framework of Hilbert space. In addition, we give a numerical example to support our main result.
在本文中，我们引入了一个新问题，即修正的分裂广义均衡问题，它扩展了广义均衡问题、分裂均衡问题和分裂变分不等式问题。我们引入了一种新的迭代格式方法，用于在不假设半闭性条件的情况下，找到变分不等式问题解集、有限族拟非扩张映射的公共不动点集以及修正的分裂广义均衡问题解集的一个公共元素，其中 是一个拟非扩张映射且 ；这是在希尔伯特空间框架下一个困难的证明。此外，我们给出一个数值例子来支持我们的主要结果。
