Linesearch algorithms for split equilibrium problems and nonexpansive mappings
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- 作者：Bui Van Dinh ; Dang Xuan Son ; Liguo Jiao ; Do Sang Kim
- 关键词：split equilibrium problem ; common fixed point problem ; nonexpansive mapping ; pseudomonotonicity ; projection method ; linesearch rule ; weak and strong convergence
- 刊名：Fixed Point Theory and Applications
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：2016
- 期：1
- 全文大小：1,662 KB
- 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
- 出版者：Springer International Publishing
- ISSN：1687-1812
文摘
In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given.