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.

scholarly journals Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving (A,m,η)-Generalized Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Jittiporn Suwannawit ◽  
Narin Petrot
Keyword(s):  
Iterative Algorithm ◽  
Monotone Operator ◽  
Existence Of Solutions ◽  
Monotone Operators ◽  
Variational Inclusion ◽  
Random Set ◽  
Inclusion Problems ◽  
Existence And Stability ◽  
The Stability

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called (A,m,η)-monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is also discussed.

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 Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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 Existence and Stability of Solutions of General Semilinear Elliptic Equations with Measure Data

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Measure Data ◽  
Unified Theory ◽  
Stability Of Solutions ◽  
Semilinear Elliptic ◽  
The Poisson Equation ◽  
Order Elliptic Operator ◽  
Carathéodory Function ◽  
Existence And Stability ◽  
The Stability

AbstractWe study existence and stability for solutions of −Lu + g(x, u) = ω where L is a second order elliptic operator, g a Caratheodory function and ω a measure in Ω. We present a unified theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

scholarly journals System of Operator Quasi Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Suhel Ahmad Khan
Keyword(s):  
Maximal Element ◽  
Equilibrium Problems ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Quasi Equilibrium ◽  
Basic Tool ◽  
Maximal Element Theorem ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Element Theorem

We consider a system of operator quasi equilibrium problems and system of generalized quasi operator equilibrium problems in topological vector spaces. Using a maximal element theorem for a family of set-valued mappings as basic tool, we derive some existence theorems for solutions to these problems with and without involving Φ-condensing mappings.

scholarly journals On the existence and stability of solutions to stochastic equilibrium problems

2020 ◽  
Author(s):  
Anh Quoc Lam ◽  
Hai Xuan Nguyen ◽  
Kien Trung Nguyen ◽  
Quan Hong Nguyen ◽  
Dang Thi My Van
Keyword(s):  
Stochastic Optimization ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Optimization Problems ◽  
Lower Semicontinuous ◽  
Probability Measures ◽  
Stability Of Solutions ◽  
Stochastic Equilibrium ◽  
Special Cases ◽  
Existence And Stability

In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing KKM-Fan xed point theorem, conditions for the existence of solutions to such problems are established. We then propose new metric concepts on the underlying stochastic spaces and study some properties corresponding to these metrics. Afterwards, we study sucient conditions for the solution mappings of such problems, that are closed, upper (lower) semicontinuous and continuous with respect to the mentioned metrics. Finally, the special cases of stochastic optimization problems are taken into account as the applications.

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