scholarly journals GENERALIZED IMPLICIT INCLUSION PROBLEMS ON NONCOMPACT SETS WITH APPLICATIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 261-279
Author(s):  
SAN-HUA WANG ◽  
NAN-JING HUANG
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Existence Results ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Inclusion Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

AbstractIn this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.

scholarly journals Extended Mixed Vector Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mijanur Rahaman ◽  
Adem Kılıçman ◽  
Rais Ahmad
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Noncompact Domain ◽  
Vector Equilibrium

We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005), some existence results for both problems are proved in noncompact domain.

scholarly journals On the convexity of the solution set of symmetric vector equilibrium problems

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2097-2105 ◽  
Author(s):  
A.P. Farajzadeh
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Solution Set ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

In this paper, without assumption of monotonicity and boundedness, we study existence results for a solution and the convexity of the solution set to the symmetric vector equilibrium problem for setvalued mappings in the setting of topological vector spaces. Our results improve the corresponding results in [9, 18, 19, 22, 28, 33, 36, 37].

scholarly journals Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ali Farajzadeh ◽  
Kasamsuk Ungchittrakool ◽  
Apisit Jarernsuk
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Variational Inequality ◽  
Vector Equilibrium Problem ◽  
Variational Inequality Problems ◽  
Vector Equilibrium Problems ◽  
Noncompact Domain ◽  
Vector Equilibrium

We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting.

scholarly journals Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Amini-Harandi ◽  
D. O'Regan
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Vector Equilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Set Valued Mapping ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium

We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

scholarly journals Strong Vector Equilibrium Problems in Topological Vector Spaces Via KKM Maps

Cubo (Temuco) ◽  
2010 ◽  
Vol 12 (1) ◽  
pp. 219-230 ◽  
Author(s):  
A.P Farajzadeh ◽  
A Amini-Harandi ◽  
O'Regan ◽  
R.P Agarwal
Keyword(s):  
Equilibrium Problems ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Kkm Maps ◽  
Vector Equilibrium

scholarly journals Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Adem Kılıçman ◽  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Equilibrium Problem ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Generalized Pseudomonotonicity

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

scholarly journals An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Wensheng Jia ◽  
Xiaoling Qiu ◽  
Dingtao Peng
Keyword(s):  
Exact Solution ◽  
Bounded Rationality ◽  
Equilibrium Problems ◽  
Approximation Theorem ◽  
Optimization Problems ◽  
Vector Equilibrium Problems ◽  
Special Cases ◽  
Full Rationality ◽  
Vector Equilibrium ◽  
Special Case

In this paper, our purpose is to investigate the vector equilibrium problem of whether the approximate solution representing bounded rationality can converge to the exact solution representing complete rationality. An approximation theorem is proved for vector equilibrium problems under some general assumptions. It is also shown that the bounded rationality is an approximate way to achieve the full rationality. As a special case, we obtain some corollaries for scalar equilibrium problems. Moreover, we obtain a generic convergence theorem of the solutions of strictly-quasi-monotone vector equilibrium problems according to Baire’s theorems. As applications, we investigate vector variational inequality problems, vector optimization problems and Nash equilibrium problems of multi-objective games as special cases.

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