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 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 A primal-dual approach of weak vector equilibrium problems

2018 ◽  
Vol 16 (1) ◽  
pp. 276-288 ◽  
Author(s):  
Szilárd László
Keyword(s):  
Original Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Dual Model ◽  
Vector Equilibrium Problems ◽  
Dual Approach ◽  
Topological Vector Spaces ◽  
Primal Dual ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we provide conditions that assure the solution set of the original problem and its dual coincide. We show that many known problems from the literature can be treated in our primal-dual model. We provide several coercivity conditions in order to obtain the existence of the solution of the primal-dual problems without compactness assumption. We apply the obtained results to perturbed vector equilibrium problems.

scholarly journals Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds

2019 ◽  
Author(s):  
Gabriel Ruiz-Garzón ◽  
Maria B. Donato ◽  
Rafaela Osuna-Gómez ◽  
Monica Milasi
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Hadamard Manifolds ◽  
Vector Equilibrium Problems ◽  
Topological Vector Spaces ◽  
Weakly Efficient Solutions ◽  
Vector Equilibrium

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

scholarly journals Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Kanokwan Sitthithakerngkiet ◽  
Somyot Plubtieng
Keyword(s):  
Equilibrium Problems ◽  
Compact Convex ◽  
Sufficient Conditions ◽  
Multivalued Mappings ◽  
Vector Equilibrium Problems ◽  
All Solutions ◽  
Nonempty Compact ◽  
Vector Equilibrium ◽  
Nonempty Compact Convex Subset ◽  
Vector Valued

LetKbe a nonempty compact convex subset of a topological vector space. In this paper-sufficient conditions are given for the existence ofx∈Ksuch thatF(T)∩VEP(F)≠∅, whereF(T)is the set of all fixed points of the multivalued mappingTandVEP(F)is the set of all solutions for vector equilibrium problem of the vector-valued mappingF. This leads us to generalize and improve some existence results in the recent references.

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 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
Sign in / Sign up

Export Citation Format

Share Document