scholarly journals Weak convergence theorem by a new extragradient method for fixed point problems and variational inequality problems

2014 ◽  
Vol 63 (1) ◽  
pp. 43-53
Author(s):  
KARAHAN İbrahim; ÖZDEMİR
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Convergence Theorem ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Fixed Point Problems ◽  
Weak Convergence Theorem

scholarly journals An Extension of Subgradient Method for Variational Inequality Problems in Hilbert Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xueyong Wang ◽  
Shengjie Li ◽  
Xipeng Kou
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Nonexpansive Mapping ◽  
Iterative Process ◽  
Subgradient Method ◽  
Variational Inequality Problems ◽  
Mild Conditions ◽  
Weak Convergence Theorem

An extension of subgradient method for solving variational inequality problems is presented. A new iterative process, which relates to the fixed point of a nonexpansive mapping and the current iterative point, is generated. A weak convergence theorem is obtained for three sequences generated by the iterative process under some mild conditions.

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