scholarly journals Existence and Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Kaihong Wang ◽  
Wenyan Zhang ◽  
Min Fang
Keyword(s):  
Existence Result ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Solution Set ◽  
Quasi Equilibrium ◽  
Well Posedness

An existence result for the solution set of symmetric vector quasi-equilibrium problems that allows for discontinuities is obtained. Moreover, sufficient conditions for the generalized Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems are established.

scholarly journals Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei-bing Zhang ◽  
Nan-jing Huang ◽  
Donal O’Regan
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

scholarly journals Metric Characterizations ofα-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
L. C. Ceng ◽  
Y. C. Lin
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Equilibrium Problems ◽  
Uniqueness Of Solution ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Special Case

The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept ofα-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations ofα-well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that theα-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept ofα-well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature.

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