Projection algorithms for the system of generalized mixed variational inequalities in Banach spaces

2011 ◽  
Vol 217 (19) ◽  
pp. 7718-7724 ◽  
Author(s):  
Qing-bang Zhang ◽  
Ru-liang Deng
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Projection Algorithms ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequalities

scholarly journals On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen ◽  
Hui-Ying Hu ◽  
Long He ◽  
...  
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space. The relations between the Levitin–Polyak well-posedness and Hadamard well-posedness for a generalized mixed variational inequality are studied. The characterizations of Hadamard well-posedness for a generalized mixed variational inequality are established.

scholarly journals Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-38
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Inclusion Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Mixed Variational Inequality ◽  
Mixed Variational Inequalities ◽  
Generalized Mixed Variational Inequality ◽  
Generalized Mixed Variational Inequalities

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.

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