Wiener-Hopf equation technique for solving equilibrium problems and variational inequalities and fixed points of a nonexpansive mapping

被引：0
作者：
Yuehu Wang
Congjun Zhang
机构：
[1] Anhui University,School of Mathematical Science
[2] Nanjing University of Finance and Economics,School of Applied Mathematics
来源：
Journal of Inequalities and Applications | / 2014卷
关键词：
equilibrium problems; algorithms; Wiener-Hopf equation technique; auxiliary principle;
D O I：
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摘要：
In this paper, we introduce some new iterative schemes based on the Wiener-Hopf equation technique and auxiliary principle for finding common elements of the set of solutions of equilibrium problems, the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality. Several strong convergence results for the sequences generated by these iterative schemes are established in Hilbert spaces. As the generation, we also consider two generalized variational inequalities, and obtain some iterative schemes and the proposed strong convergence theorems for solving these generalized variational inequalities, equilibrium problems, and a nonexpansive mapping. Our results and proof are new, and they extend the corresponding results of Verma (Appl. Math. Lett. 10:107-109, 1997), Wu and Li (4th International Congress on Image and Signal Processing, pp. 2802-2805, 2011), and Noor and Huang (Appl. Math. Comput. 191:504-510, 2007).
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