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 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 Solving split generalized mixed equality equilibrium problems and split equality fixed point problems for nonexpansive-type maps

2020 ◽  
Vol 36 (1) ◽  
pp. 119-126
Author(s):  
M. O. NNAKWE
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Real Banach Space ◽  
Equilibrium Problems ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Uniformly Convex ◽  
Type Condition ◽  
Common Solution ◽  
Uniformly Smooth

"Let X be a 2-uniformly convex and uniformly smooth real Banach space. In this paper, an iterative algorithmofKrasnosel’skii-typeis constructed and used to approximate a common solution ofsplit generalized mixed equalityequilibrium problems(SGMEEP)andsplit equality fixed point problems(SEFPP)forquasi-ψ-nonexpansive maps.A strong convergence theorem of the sequence generated by this algorithm is proved without imposing anycompactness-type condition on either the operators or the space considered. The theorem proved improves andcomplements important recent results in the literature. "

scholarly journals A nonsmooth Stackelberg equilibrium problem via mixed variational inequalities

2019 ◽  
Vol 35 (3) ◽  
pp. 339-347
Author(s):  
JUE LU ◽  
◽  
LI-WEN ZHOU ◽  
YI-BIN XIAO ◽  
NAN-JING HUANG ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Operator Method ◽  
Stackelberg Equilibrium ◽  
Banach Fixed Point Theorem ◽  
Best Response ◽  
Mixed Variational Inequalities ◽  
The Resolvent Operator

In this paper, we introduce and study a class of nonsmooth Stackelberg equilibrium problems with differential revenue functions and nonsmooth cost functions. First, we describe the best response set of the follower and the best strategy set of the leader for the considered nonsmooth Stackelberg equilibrium problem via mixed variational inequalities. Then, by using the resolvent operator method and the Banach fixed point theorem, we show the existence and uniqueness of its solution.

scholarly journals On existence of a solution for the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps

2005 ◽  
Vol 2005 (15) ◽  
pp. 2409-2420 ◽  
Author(s):  
Jianwen Peng ◽  
Xinmin Yang
Keyword(s):  
Equilibrium Problems ◽  
Existence Results ◽  
Quasi Equilibrium ◽  
Existence Of A Solution ◽  
New Model ◽  
Upper Semicontinuous ◽  
Special Cases

We introduce a new model of the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps and present several existence results of a solution for this system of generalized vector quasi-equilibrium problems and its special cases. The results in this paper extend and improve some results in the literature.

Well-Posedness for Parametric Generalized Strong Vector Quasi-Equilibrium Problem

2014 ◽  
Vol 556-562 ◽  
pp. 4093-4096
Author(s):  
Ya Li Zhao ◽  
Lin Zhu
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Well Posedness

In this paper, well-posedness for parametric generalized strong vector quasi-equilibrium problems is studied. The corresponding concept of well-posedness in the generalized sense is also investigated for the parametric generalized strong vector quasi-equilibrium problem. Under some suitable conditions, we establish some characterizations of well-posedness for the parametric generalized strong vector quasi-equilibrium problem.

scholarly journals Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

2021 ◽  
Vol 37 (3) ◽  
pp. 393-406
Author(s):  
SULIMAN AL-HOMIDAN ◽  
◽  
QAMRUL HASAN ANSARI ◽  
MONIRUL ISLAM ◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Coercivity Conditions ◽  
Hadamard Manifolds ◽  
Type Condition ◽  
Proximal Point ◽  
Strong Pseudomonotonicity

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

A Stackelberg quasi-equilibrium problem via quasi-variational inequalities

2018 ◽  
Vol 34 (3) ◽  
pp. 355-362
Author(s):  
JUE LU ◽  
◽  
YI-BIN XIAO ◽  
NAN-JING HUANG ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Quasi Equilibrium ◽  
Quasivariational Inequality ◽  
Finite Dimensional ◽  
Inequality Techniques

In this paper, we consider a class of Stackelberg quasi-equilibrium problem with two players in finite dimensional spaces. Existence and location of the Stackelberg quasi-equilibrium is discussed by employing the quasivariational inequality techniques and the fixed point arguments. The results presented in this paper generalize some corresponding ones due to Nagy [Nagy, S., Stackelberg equilibia via variational inequalities and projections, J. Global Optim., 57 (2013), 821–828].

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.

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