# Stability of solution mappings for parametric bilevel vector equilibrium problems

## Abstract

In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints.

- Authors:

- Can Tho University, Department of Mathematics, Teacher College (Viet Nam)
- Ton Duc Thang University, Department for Management of Science and Technology Development (Viet Nam)

- Publication Date:

- OSTI Identifier:
- 22769339

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; EQUILIBRIUM; MATHEMATICAL SOLUTIONS; OPTIMIZATION; VARIATIONAL METHODS

### Citation Formats

```
Anh, Lam Quoc, E-mail: quocanh@ctu.edu.vn, and Hung, Nguyen Van, E-mail: nguyenvanhung2@tdt.edu.vn.
```*Stability of solution mappings for parametric bilevel vector equilibrium problems*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0411-Z.

```
Anh, Lam Quoc, E-mail: quocanh@ctu.edu.vn, & Hung, Nguyen Van, E-mail: nguyenvanhung2@tdt.edu.vn.
```*Stability of solution mappings for parametric bilevel vector equilibrium problems*. United States. doi:10.1007/S40314-016-0411-Z.

```
Anh, Lam Quoc, E-mail: quocanh@ctu.edu.vn, and Hung, Nguyen Van, E-mail: nguyenvanhung2@tdt.edu.vn. Tue .
"Stability of solution mappings for parametric bilevel vector equilibrium problems". United States. doi:10.1007/S40314-016-0411-Z.
```

```
@article{osti_22769339,
```

title = {Stability of solution mappings for parametric bilevel vector equilibrium problems},

author = {Anh, Lam Quoc, E-mail: quocanh@ctu.edu.vn and Hung, Nguyen Van, E-mail: nguyenvanhung2@tdt.edu.vn},

abstractNote = {In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints.},

doi = {10.1007/S40314-016-0411-Z},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.