On system of generalized vector quasi-equilibrium problems with set-valued maps

Jian Wen Peng; Heung Wing Joseph Lee; Xin Min Yang

doi:10.1007/s10898-006-9004-5

On system of generalized vector quasi-equilibrium problems with set-valued maps

Jian Wen Peng, Heung Wing Joseph Lee, Xin Min Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

14 Citations (Scopus)

Abstract

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.

Original language	English
Pages (from-to)	139-158
Number of pages	20
Journal	Journal of Global Optimization
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s10898-006-9004-5
Publication status	Published - 1 Sept 2006

Keywords

Φ-condensing map
C -0-partially diagonally quasiconvex i-x
Generalized Debreu type equilibrium problem
Maximal element theorem
System of generalized vector quasi-equilibrium problems
System of vector quasi-equilibrium problems

ASJC Scopus subject areas

Computer Science Applications
Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1007/s10898-006-9004-5

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abstract = "In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.",

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AU - Peng, Jian Wen

AU - Lee, Heung Wing Joseph

AU - Yang, Xin Min

PY - 2006/9/1

Y1 - 2006/9/1

N2 - In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.

AB - In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.

KW - Φ-condensing map

KW - C -0-partially diagonally quasiconvex i-x

KW - Generalized Debreu type equilibrium problem

KW - Maximal element theorem

KW - System of generalized vector quasi-equilibrium problems

KW - System of vector quasi-equilibrium problems

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DO - 10.1007/s10898-006-9004-5

M3 - Journal article

SN - 0925-5001

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SP - 139

EP - 158

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 1

ER -

On system of generalized vector quasi-equilibrium problems with set-valued maps

Abstract

Keywords

ASJC Scopus subject areas

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