scholarly journals Tangent Projection Equations and General Variational Inequalities

2001 ◽  
Vol 258 (2) ◽  
pp. 755-762 ◽  
Author(s):  
Naihua Xiu ◽  
Jianzhong Zhang ◽  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
General Variational Inequalities ◽  
Projection Equations

scholarly journals System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 198
Author(s):  
Kyung Kim
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Projection Method ◽  
Equivalent Problem ◽  
Nonlinear Operators ◽  
Nonlinear Projection ◽  
General Variational Inequalities ◽  
Projection Equations

In this manuscript, we study a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed ( α , r ) -cocoercive mappings. Using the projection method, we show that a system of extended general variational inequalities is equivalent to the nonlinear projection equations. This alternative equivalent problem is used to consider the existence and convergence (or approximate solvability) of a solution of a system of extended general variational inequalities under suitable conditions.

scholarly journals Parametric Extended General Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problems ◽  
Equivalent Formulation ◽  
Resolvent Equations ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Significant Extension ◽  
Mixed Variational Inequalities ◽  
The Given

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational inequalities, quasi (mixed) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results.

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