On a Class of Generalized Vector Quasiequilibrium Problems with Set-Valued Maps

2008 ◽  
Vol 139 (2) ◽  
pp. 337-350 ◽  
Author(s):  
P. H. Sach
Keyword(s):  
Quasiequilibrium Problems ◽  
Vector Quasiequilibrium Problems

scholarly journals Painleve-Kuratowski convergences of the approximate solution sets for vector quasiequilibrium problems

2018 ◽  
Vol 34 (1) ◽  
pp. 115-122
Author(s):  
NGUYEN VAN HUNG ◽  
◽  
DINH HUY HOANG ◽  
VO MINH TAM ◽  
◽  
...  
Keyword(s):  
Approximate Solution ◽  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Special Cases ◽  
Vector Quasiequilibrium Problems

In this paper, we study vector quasiequilibrium problems. After that, the Painlev´e-Kuratowski upper convergence, lower convergence and convergence of the approximate solution sets for these problems are investigated by using a sequence of mappings ΓC -converging. As applications, we also consider the Painlev´e-Kuratowski upper convergence of the approximate solution sets in the special cases of variational inequality problems of the Minty type and Stampacchia type. The results presented in this paper extend and improve some main results in the literature.

scholarly journals Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Shu-qiang Shan ◽  
Yu Han ◽  
Nan-jing Huang
Keyword(s):  
Nash Equilibria ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Upper Semicontinuity ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Quasiequilibrium Problems ◽  
Parametric Variational Inequality ◽  
Parametric Optimization Problem ◽  
Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.

scholarly journals The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qi-Qing Song
Keyword(s):  
Equilibrium Problem ◽  
Existence Result ◽  
Quasi Equilibrium ◽  
Topological Order ◽  
Stability Of Solutions ◽  
Maximal Elements ◽  
Quasiequilibrium Problems ◽  
Existence And Stability ◽  
Essential Set ◽  
Vector Quasiequilibrium Problems

In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem.

scholarly journals On System of Generalized Vector Quasiequilibrium Problems with Applications

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Jian-Wen Peng ◽  
Lun Wan
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Quasi Equilibrium ◽  
Vector Equilibrium Problems ◽  
Quasiequilibrium Problems ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems ◽  
Vector Valued Functions ◽  
Vector Valued

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions.

scholarly journals Hölder Continuity of Solutions to Parametric Generalized Vector Quasiequilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Y. Peng
Keyword(s):  
Recent Literature ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Holder Continuity ◽  
Quasiequilibrium Problems ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Quasiequilibrium Problems ◽  
Quasiequilibrium Problem ◽  
Vector Quasiequilibrium Problem

By using a linear scalarization method, we establish sufficient conditions for the Hölder continuity of the solution mappings to a parametric generalized vector quasiequilibrium problem with set-valued mappings. These results extend the recent ones in the recent literature, (e.g., Li et al. (2009), Li et al. (2011)). Furthermore, two examples are given to illustrate the obtained result.

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