scholarly journals Onη-Upper Sign Property and Upper Sign Continuity and Their Applications in Equilibrium-Like Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ali Farajzadeh ◽  
Somaye Jafari ◽  
Chin-Tzong Pang
Keyword(s):  
Equilibrium Problem ◽  
Local Equilibrium ◽  
Existence Results ◽  
Solution Sets ◽  
Sign Property ◽  
Upper Sign Property

We first introduce the notion ofη-upper sign property which is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium problem) and equilibrium problem for mappings whose domains are not necessarily convex by relaxing the upper sign continuity on the map, as it is assumed in the literature (Bianchi and Pini, 2005; Castellani and Giuli, 2013; Farajzadeh and Zafarani, 2010). Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.

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 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 Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

2021 ◽  
Author(s):  
M. Bianchi ◽  
G. Kassay ◽  
R. Pini
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Penalty Method ◽  
Real Banach Space ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Quasi Equilibrium ◽  
Coercivity Conditions ◽  
Usual Equilibrium

AbstractIn this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

scholarly journals Constrained Weak Nash-Type Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
W. C. Shuai ◽  
K. L. Xiang ◽  
W. Y. Zhang
Keyword(s):  
Existence Theorem ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function ◽  
Payoff Functions

A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. The results extend the corresponding one of Fu (2003). In particular, if the payoff functions are singlevalued, our existence theorem extends the main results of Fu (2003) by relaxing the assumption of convexity.

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.

Existence Results in a General Equilibrium Problem

2013 ◽  
Vol 34 (4) ◽  
pp. 430-450 ◽  
Author(s):  
Le Anh Tuan ◽  
Pham Huu Sach ◽  
Nguyen Ba Minh
Keyword(s):  
General Equilibrium ◽  
Equilibrium Problem ◽  
Existence Results

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].

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