Generalized vector quasi-variational inequality problems over product sets

Q. H. Ansari; S. Schaible; J. C. Yao

doi:10.1007/s10898-003-2682-3

Generalized vector quasi-variational inequality problems over product sets

Q. H. Ansari^*
, S. Schaible
, J. C. Yao

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.

Original language	English
Pages (from-to)	437-449
Number of pages	13
Journal	Journal of Global Optimization
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s10898-003-2682-3
State	Published - Aug 2005

Bibliographical note

Funding Information:
The authors are grateful to the referees for their valuable comments and suggestions. In this research, the first author was partially supported by the Major Research Project of University Grants Commission, No. F. 8-1/2002 (SR-1), New Delhi, Govt. of India while the third author was supported by the National Science Council of the Republic of China. The first author is also grateful to the Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia for providing excellent research facilities to carry out this work.

Keywords

Generalized vector quasi-variational inequalities
Relatively maximal pseudomonotone maps
Relatively pseudomonotone maps
Systems of generalized vector quasi-variational inequalities
Systems of vector quasi-variational inequalities

ASJC Scopus subject areas

Business, Management and Accounting (miscellaneous)
Computer Science Applications
Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1007/s10898-003-2682-3

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title = "Generalized vector quasi-variational inequality problems over product sets",

abstract = "In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.",

keywords = "Generalized vector quasi-variational inequalities, Relatively maximal pseudomonotone maps, Relatively pseudomonotone maps, Systems of generalized vector quasi-variational inequalities, Systems of vector quasi-variational inequalities",

author = "Ansari, \{Q. H.\} and S. Schaible and Yao, \{J. C.\}",

note = "Funding Information: The authors are grateful to the referees for their valuable comments and suggestions. In this research, the first author was partially supported by the Major Research Project of University Grants Commission, No. F. 8-1/2002 (SR-1), New Delhi, Govt. of India while the third author was supported by the National Science Council of the Republic of China. The first author is also grateful to the Department of Mathematical Sciences, King Fahd University of Petroleum \& Minerals, Dhahran, Saudi Arabia for providing excellent research facilities to carry out this work.",

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doi = "10.1007/s10898-003-2682-3",

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AU - Ansari, Q. H.

AU - Schaible, S.

AU - Yao, J. C.

N1 - Funding Information: The authors are grateful to the referees for their valuable comments and suggestions. In this research, the first author was partially supported by the Major Research Project of University Grants Commission, No. F. 8-1/2002 (SR-1), New Delhi, Govt. of India while the third author was supported by the National Science Council of the Republic of China. The first author is also grateful to the Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia for providing excellent research facilities to carry out this work.

PY - 2005/8

Y1 - 2005/8

N2 - In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.

AB - In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.

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KW - Relatively maximal pseudomonotone maps

KW - Relatively pseudomonotone maps

KW - Systems of generalized vector quasi-variational inequalities

KW - Systems of vector quasi-variational inequalities

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ER -

Generalized vector quasi-variational inequality problems over product sets

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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