scholarly journals Unified vector quasiequilibrium problems via improvement sets and nonlinear scalarization with stability analysis

2020 ◽  
Vol 10 (1) ◽  
pp. 107-125
Author(s):  
Hong-Zhi Wei ◽  
◽  
Xin Zuo ◽  
Chun-Rong Chen ◽  
Keyword(s):  
Stability Analysis ◽  
Nonlinear Scalarization ◽  
Quasiequilibrium Problems ◽  
Improvement Sets ◽  
Vector Quasiequilibrium Problems

Stability analysis for vector quasiequilibrium problems

Positivity ◽  
2012 ◽  
Vol 17 (3) ◽  
pp. 365-379 ◽  
Author(s):  
Xiaodong Fan ◽  
Caozong Cheng ◽  
Haijun Wang
Keyword(s):  
Stability Analysis ◽  
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.

Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

2020 ◽  
Vol 37 (04) ◽  
pp. 2040003
Author(s):  
Zai-Yun Peng ◽  
Jing-Jing Wang ◽  
Xian-Jun Long ◽  
Fu-Ping Liu
Keyword(s):  
Efficient Solution ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Solution Sets ◽  
Improvement Sets ◽  
Oriented Distance ◽  
Kuratowski Convergence ◽  
Symmetric Set ◽  
Convergence Of Solution

This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)[Formula: see text] via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)[Formula: see text] are obtained through a new nonlinear scalarization technical. Then, under [Formula: see text]-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)[Formula: see text] is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)[Formula: see text] under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

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.

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