Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities

2004 ◽  
Vol 122 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. Bianchi ◽  
N. Hadjisavvas ◽  
S. Schaible
Keyword(s):  
Variational Inequalities ◽  
Coercivity Conditions ◽  
Exceptional Families Of Elements ◽  
Exceptional Families

scholarly journals Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

2021 ◽  
Author(s):  
M. Bianchi ◽  
G. Kassay ◽  
R. Pini
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Penalty Method ◽  
Real Banach Space ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Quasi Equilibrium ◽  
Coercivity Conditions ◽  
Usual Equilibrium

AbstractIn this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

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.

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