System of vector quasi-variational inclusions with some applications

Lai Jiu Lin; Qamrul Hasan Ansari; Yu Jen Huang

doi:10.1016/j.na.2007.08.053

System of vector quasi-variational inclusions with some applications

Lai Jiu Lin^*
, Qamrul Hasan Ansari
, Yu Jen Huang

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

6 Scopus citations

Abstract

In this paper, we consider systems of vector quasi-variational inclusions which include systems of vector quasi-equilibrium problems for multivalued maps, systems of vector optimization problems and several other systems as special cases. We establish existence results for solutions of these systems. As applications of our results, we derive the existence results for solutions of system vector optimization problems, mathematical programs with systems of vector variational inclusion constraints and bilevel problems. Another application of our results provides the common fixed point theorem for a family of lower semicontinuous multivalued maps. Further applications of our results for existence of solutions of systems of vector quasi-variational inclusions are given to prove the existence of solutions of systems of Minty type and Stampacchia type generalized implicit quasi-variational inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

Original language	English
Pages (from-to)	2812-2824
Number of pages	13
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	69
Issue number	9
DOIs	https://doi.org/10.1016/j.na.2007.08.053
State	Published - 1 Nov 2008

Bibliographical note

Funding Information:
Acknowledgements. The authors would like to acknowledge the support of the Army Research Institute (ARI) for the funding of this work. Opinions expressed are those of the authors and do not necessarily represent an official position of the Department of the Army or the Army Research Institute.

Keywords

Bilevel problem
Common fixed point theorem
Mathematical programs with systems of vector variational inclusion constraints
Systems of vector quasi-equilibrium problems
Systems of vector variational inclusions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2007.08.053

Cite this

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title = "System of vector quasi-variational inclusions with some applications",

abstract = "In this paper, we consider systems of vector quasi-variational inclusions which include systems of vector quasi-equilibrium problems for multivalued maps, systems of vector optimization problems and several other systems as special cases. We establish existence results for solutions of these systems. As applications of our results, we derive the existence results for solutions of system vector optimization problems, mathematical programs with systems of vector variational inclusion constraints and bilevel problems. Another application of our results provides the common fixed point theorem for a family of lower semicontinuous multivalued maps. Further applications of our results for existence of solutions of systems of vector quasi-variational inclusions are given to prove the existence of solutions of systems of Minty type and Stampacchia type generalized implicit quasi-variational inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.",

keywords = "Bilevel problem, Common fixed point theorem, Mathematical programs with systems of vector variational inclusion constraints, Systems of vector quasi-equilibrium problems, Systems of vector variational inclusions",

author = "Lin, \{Lai Jiu\} and Ansari, \{Qamrul Hasan\} and Huang, \{Yu Jen\}",

note = "Funding Information: Acknowledgements. The authors would like to acknowledge the support of the Army Research Institute (ARI) for the funding of this work. Opinions expressed are those of the authors and do not necessarily represent an official position of the Department of the Army or the Army Research Institute.",

year = "2008",

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doi = "10.1016/j.na.2007.08.053",

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T1 - System of vector quasi-variational inclusions with some applications

AU - Lin, Lai Jiu

AU - Ansari, Qamrul Hasan

AU - Huang, Yu Jen

N1 - Funding Information: Acknowledgements. The authors would like to acknowledge the support of the Army Research Institute (ARI) for the funding of this work. Opinions expressed are those of the authors and do not necessarily represent an official position of the Department of the Army or the Army Research Institute.

PY - 2008/11/1

Y1 - 2008/11/1

N2 - In this paper, we consider systems of vector quasi-variational inclusions which include systems of vector quasi-equilibrium problems for multivalued maps, systems of vector optimization problems and several other systems as special cases. We establish existence results for solutions of these systems. As applications of our results, we derive the existence results for solutions of system vector optimization problems, mathematical programs with systems of vector variational inclusion constraints and bilevel problems. Another application of our results provides the common fixed point theorem for a family of lower semicontinuous multivalued maps. Further applications of our results for existence of solutions of systems of vector quasi-variational inclusions are given to prove the existence of solutions of systems of Minty type and Stampacchia type generalized implicit quasi-variational inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

AB - In this paper, we consider systems of vector quasi-variational inclusions which include systems of vector quasi-equilibrium problems for multivalued maps, systems of vector optimization problems and several other systems as special cases. We establish existence results for solutions of these systems. As applications of our results, we derive the existence results for solutions of system vector optimization problems, mathematical programs with systems of vector variational inclusion constraints and bilevel problems. Another application of our results provides the common fixed point theorem for a family of lower semicontinuous multivalued maps. Further applications of our results for existence of solutions of systems of vector quasi-variational inclusions are given to prove the existence of solutions of systems of Minty type and Stampacchia type generalized implicit quasi-variational inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

KW - Bilevel problem

KW - Common fixed point theorem

KW - Mathematical programs with systems of vector variational inclusion constraints

KW - Systems of vector quasi-equilibrium problems

KW - Systems of vector variational inclusions

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DO - 10.1016/j.na.2007.08.053

M3 - Article

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SN - 0362-546X

VL - 69

SP - 2812

EP - 2824

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 9

ER -

System of vector quasi-variational inclusions with some applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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