scholarly journals Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
De-ning Qu ◽  
Cao-zong Cheng
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Inclusion Problem ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Topological Vector Spaces ◽  
Variational Inclusion Problem ◽  
Scalarization Method ◽  
Scalarization Function ◽  
Locally Convex

The aim of this paper is to study generalized vector quasi-equilibrium problems (GVQEPs) by scalarization method in locally convex topological vector spaces. A general nonlinear scalarization function for set-valued mappings is introduced, its main properties are established, and some results on the existence of solutions of the GVQEPs are shown by utilizing the introduced scalarization function. Finally, a vector variational inclusion problem is discussed as an application of the results of GVQEPs.

scholarly journals Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei-bing Zhang ◽  
Nan-jing Huang ◽  
Donal O’Regan
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

scholarly journals Existence of solutions for a new version of generalized operator equilibrium problems

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4701-4710
Author(s):  
Ardeshir Karamian ◽  
Rahmatollah Lashkaripour
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Existence Result ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Nonlinear Scalarization ◽  
Topological Vector Spaces ◽  
Generalized Operator ◽  
Ky Fan

In this paper, a system of generalized operator equilibrium problems(for short, SGOEP) in the setting of topological vector spaces is introduced. Applying some properties of the nonlinear scalarization mapping and the maximal element lemma an existence theorem for SGOEP is proved. Moreover, using Ky Fan?s lemma an existence result for the generalized operator equilibrium problem(for short, GOEP) is established. The results of the paper can be viewed as a generalization and improvement of the corresponding results given in [1,2,5,8].

scholarly journals On System of Generalized Vector Quasiequilibrium Problems with Applications

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Jian-Wen Peng ◽  
Lun Wan
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Quasi Equilibrium ◽  
Vector Equilibrium Problems ◽  
Quasiequilibrium Problems ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems ◽  
Vector Valued Functions ◽  
Vector Valued

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions.

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