scholarly journals AN ITERATIVE METHOD FOR GENERALIZED MIXED VECTOR EQUILIBRIUM PROBLEMS AND FIXED POINT OF NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITIES

2012 ◽  
Vol 16 (5) ◽  
pp. 1681-1705 ◽  
Author(s):  
Shu-qiang Shan ◽  
Nan-jing Huang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium

scholarly journals Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Qiao-Li Dong ◽  
Yan-Ni Guo ◽  
Fang Su
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
General System ◽  
Countable Family ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
System Of Variational Inequalities

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.

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