scholarly journals Application of penalty methods to generalized variational inequalities in Banach spaces

2017 ◽  
Vol 10 (10) ◽  
pp. 5311-5320
Author(s):  
G. W. Su ◽  
Z. W. Zhao
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Penalty Methods ◽  
Generalized Variational Inequalities

scholarly journals The Penalty Method for a New System of Generalized Variational Inequalities

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Yu-Chao Tang ◽  
Li-Wei Liu
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Penalty Method ◽  
Existence Of Solution ◽  
Penalty Methods ◽  
Generalized Variational Inequalities ◽  
New System

We consider a new system of generalized variational inequalities (SGVI). Using the penalty methods, we prove the existence of solution of SGVI in Hilbert spaces. Our results extend and improve some known results.

scholarly journals Solvability of Some Perturbed Generalized Variational Inequalities in Reflexive Banach Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xue-ping Luo
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Coercivity Conditions ◽  
Reflexive Banach Spaces ◽  
Generalized Variational Inequalities ◽  
Constraint Set

This paper aims to discuss the solvability of some perturbed generalized variational inequalities with both the mapping and the constraint set perturbed simultaneously in reflexive Banach spaces, under some coercivity conditions. In particular, a new result that the set is directional perturbed is presented. The main results generalize and extend some known results in this area.

scholarly journals Modified Noor's Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Shunhou Fan ◽  
Shin Min Kang ◽  
Muhammad Aslam Noor ◽  
Yonghong Yao
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Extragradient Method ◽  
Sunny Nonexpansive Retraction ◽  
Extragradient Methods ◽  
Generalized Variational Inequalities

Motivated and inspired by Korpelevich's and Noor's extragradient methods, we suggest an extragradient method by using the sunny nonexpansive retraction which has strong convergence for solving the generalized variational inequalities in Banach spaces.

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