Painlevé–Kuratowski convergences of the solution sets for generalized vector quasi-equilibrium problems

2017 ◽  
Vol 37 (3) ◽  
pp. 3832-3845 ◽  
Author(s):  
Lam Quoc Anh ◽  
Thanatporn Bantaojai ◽  
Nguyen Van Hung ◽  
Vo Minh Tam ◽  
Rabian Wangkeeree
Keyword(s):  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Solution Sets

scholarly journals Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1604
Author(s):  
Jing-Nan Li ◽  
San-Hua Wang ◽  
Yu-Ping Xu
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Saddle Points ◽  
Upper Semicontinuity ◽  
Quasi Equilibrium ◽  
Solution Sets ◽  
Variable Ordering ◽  
Variable Ordering Structures ◽  
The One ◽  
Cone Convexity

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

scholarly journals Existence conditions for symmetric strong vector quasi-equilibrium problems

2020 ◽  
Vol 3 (SI3) ◽  
pp. first
Author(s):  
Xuân Đại Lê ◽  
Hung Nguyen Van
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Quasi Equilibrium ◽  
Huge Number ◽  
Solution Sets ◽  
Quasi Variational Inequality ◽  
Existence Conditions ◽  
Number Of Authors

In the following paper, the symmetric strong vector quasi-equilibrium problems will be studied thoroughly. Afterward, the existence conditions of solution sets for these problems has been established. The results which are presented in this paper improve and extend the main results mentioned in the literature. Our results can be illustrated by some interesting examples. In 1994, Noor and Oettli introduced the following the symmetric scalar quasi-equilibrium problem. This problem is one of the generalization of the symmetric scalar quasi-equilibrium problem which is presented by Noor and Oettli. Since then, the symmetric vector quasi-equilibrium problem has been investigated by a huge number of authors in different ways. The research works mentioned above are one of our motivation to improve and extend the problem. So, in this paper, we will introduce the vector quasi-equilibrium problems. Afterward, some existence conditions of solution sets for these problems will be established. The symmetric vector quasi-equilibrium problems consist of many optimization - related models namely symmetric vector quasi-variational inequality problems, fixed point problems, coincidence-point problems and complementarity problems, etc. In recent years, a lot of results for existence of solutions for symmetric vector quasi-equilibrium problems, vector quasi-equilibrium problems, vector quasivariational inequality problems and optimization problems have been established by many authors in different ways. We will present our work in the following steps. In the first section of our paper, we will introduce the model of symmetric vector quasi-equilibrium problems. In the following section, we recall definitions, lemmas which can be used for the main results. In the last section, we will establish some conditions for existence and closedness of the solutions set by applying fixed-point theorem for symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results. Hence our results, Theorem 3.1 and Theorem 3.6 have significant improvements.

scholarly journals The existence and stability of solutions for symmetric generalized quasi-variational inclusion problems

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2147-2165 ◽  
Author(s):  
Lam Anh ◽  
Hung van
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Variational Inclusion ◽  
Quasi Equilibrium ◽  
Stability Of Solutions ◽  
Inclusion Problems ◽  
Solution Sets ◽  
Existence And Stability ◽  
The Stability

In this paper, we study the symmetric generalized quasi-variational inclusion problems. Then, we establish some existence theorems of solution sets for these problems. Moreover, the stability of solutions for these problems are also onbtained. Finally, we apply these results to symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results.

A Newton-type method for quasi-equilibrium problems and applications

Optimization ◽  
2021 ◽  
pp. 1-26
Author(s):  
Pedro Jorge S. Santos ◽  
Paulo Sérgio M. Santos ◽  
Susana Scheimberg
Keyword(s):  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Type Method

Mixed generalized quasi-equilibrium problems

2012 ◽  
Vol 56 (2) ◽  
pp. 647-667 ◽  
Author(s):  
Truong Thi Thuy Duong
Keyword(s):  
Equilibrium Problems ◽  
Quasi Equilibrium
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