A new iterative scheme with nonexpansive mappings for equilibrium problems

Journal of inequalities and applications

Anh PN¹ 

关键词: Equilibrium problems;    nonexpansive mappings;    monotone;    Lipschitz-type continuous;    fixed point;   

DOI  :  10.1186/1029-242X-2012-116

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we suggest a new iteration scheme for finding a common of the solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed points of a nonexpansive mapping. The scheme is based on both hybrid method and extragradient-type method. We obtain a strong convergence theorem for the sequences generated by these processes in a real Hilbert space. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in the literature. AMS 2010 Mathematics subject classification: 65 K10, 65 K15, 90 C25, 90 C33.

【 授权许可】

CC BY