scholarly journals Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems

2018 ◽  
Vol 14 (1) ◽  
pp. 65-79 ◽  
Author(s):  
Lam Quoc Anh ◽  
◽  
Nguyen Van Hung ◽  
◽  
Keyword(s):  
Gap Functions ◽  
Quasiequilibrium Problems ◽  
Hausdorff Continuity ◽  
Vector Quasiequilibrium Problems

scholarly journals Error bounds for generalized mixed weak vector quasiequilibrium problems via regularized gap functions

2019 ◽  
Vol 16 (3) ◽  
pp. 91
Author(s):  
Vo Minh Tam ◽  
Nguyen Huynh Vu Duy ◽  
Nguyen Kim Phat
Keyword(s):  
Error Bounds ◽  
Gap Functions ◽  
Quasiequilibrium Problems ◽  
Vector Quasiequilibrium Problems ◽  
Regularized Gap Functions ◽  
Weak Vector

This paper introduces regularized gap functions for a class of generalized mixed weak vector quasiequilibrium problems. Then, error boundsfor the concerning problems via regularized gap functions are established. Someexamples are provided to illustrate the results.

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.

Sign in / Sign up

Export Citation Format

Share Document