Linesearch algorithms for split equilibrium problems and nonexpansive mappings

Fixexd point theory and applications

Dang Xuan Son¹  Do Sang Kim¹  Bui Van Dinh²  Liguo Jiao³ 

[1] Department of Applied Mathematics, Pukyong National University, Busan, Korea;Faculty of Information Technology, Le Quy Don Technical University, Hanoi, Vietnam;Technical University, Hanoi, Vietnam

关键词: split equilibrium problem;    common fixed point problem;    nonexpansive mapping;    pseudomonotonicity;    projection method;    linesearch rule;    weak and strong convergence;    47H09;    47J25;    65K10;    65K15;    90C99;   

DOI  :  10.1186/s13663-016-0518-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY