Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems

被引：0
作者：
Zhangsong Yao
Yeong-Cheng Liou
Li-Jun Zhu
Ching-Hua Lo
Chen-Chang Wu
机构：
[1] Nanjing Xiaozhuang University,School of Information Engineering
[2] Cheng Shiu University,Department of Information Management
[3] Kaohsiung Medical University,Center for General Education
[4] Beifang University of Nationalities,School of Mathematics and Information Science
来源：
Journal of Inequalities and Applications | / 2015卷
关键词：
nonexpansive mapping; equilibrium problem; fixed point; variational inequality; 49J30; 47H09; 47H20;
D O I：
暂无
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学科分类号：
摘要：
In this paper, we first introduce an iterative algorithm for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem, and the solution set of the variational inequality problem for a monotone mapping in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets under some mild conditions.
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共 65 条
[1]  
Blum E(1994)From optimization and variational inequalities to equilibrium problems Math. Stud. 63 123-145
[2]  
Oettli W(1994)On general nonlinear complementarity problems and quasi equilibria Matematiche 49 313-331
[3]  
Noor MA(2004)On equilibrium problems Appl. Math. E-Notes 4 125-132
[4]  
Oettli W(2006)Fundamentals of equilibrium problems Math. Inequal. Appl. 9 529-566
[5]  
Noor MA(2005)Equilibrium programming in Hilbert spaces J. Nonlinear Convex Anal. 6 117-136
[6]  
Noor KI(2006)Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings J. Optim. Theory Appl. 128 191-201
[7]  
Noor MA(2009)On iterative methods for equilibrium problems Nonlinear Anal. 70 497-507
[8]  
Combettes PL(1997)Equilibrium programming using proximal-like algorithms Math. Program. 78 29-41
[9]  
Hirstoaga SA(2007)Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces J. Math. Anal. Appl. 331 506-515
[10]  
Nadezhkina N(2009)Mixed equilibrium problems and optimization problems J. Math. Anal. Appl. 352 319-329
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