Scalarized system of nonsmooth vector quasi-variational inequalities with applications to Debreu type vector equilibrium problems

Mohammed M. Alshahrani

doi:10.1186/s13660-015-0656-x

Scalarized system of nonsmooth vector quasi-variational inequalities with applications to Debreu type vector equilibrium problems

Mohammed M. Alshahrani^*

^*Corresponding author for this work

Department of Mathematics

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

Abstract

In this work, we utilize a scalarization method to introduce a system of nonsmooth vector quasi-variational inequalities. We also study their relationship to Debreu type vector equilibrium problems. Then we establish some existence results for solutions of these systems by using maximal element theorems for a family of set-valued maps.

Original language	English
Journal	Journal of Inequalities and Applications
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13660-015-0656-x
State	Published - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015, Alshahrani; licensee Springer.

Keywords

Clarke generalized directional derivative
maximal element theorem
scalarization
system of Debreu type equilibrium problem for vector-valued functions
system of nonsmooth vector quasi-variational inequalities
system of vector quasi-equilibrium problems
Φ-condensing maps

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1186/s13660-015-0656-x

Cite this

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abstract = "In this work, we utilize a scalarization method to introduce a system of nonsmooth vector quasi-variational inequalities. We also study their relationship to Debreu type vector equilibrium problems. Then we establish some existence results for solutions of these systems by using maximal element theorems for a family of set-valued maps.",

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KW - Clarke generalized directional derivative

KW - maximal element theorem

KW - scalarization

KW - system of Debreu type equilibrium problem for vector-valued functions

KW - system of nonsmooth vector quasi-variational inequalities

KW - system of vector quasi-equilibrium problems

KW - Φ-condensing maps

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JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

ER -

Scalarized system of nonsmooth vector quasi-variational inequalities with applications to Debreu type vector equilibrium problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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