Taiwanese Journal of Mathematics

SYSTEMS OF PARAMETRIC STRONG QUASI-EQUILIBRIUM PROBLEMS: EXISTENCE AND WELL-POSEDNESS ASPECTS

Jia-wei Chen and Yeong-Cheng Liou

Full-text: Open access

Abstract

In this article, we investigate the existence of solutions and Levitin-Polyak well-posedness for a class of system of parametric strong quasi-equilibrium problems (SPSQEP) involving set-valued mappings in Hausdorff topological vector spaces. The existence of solutions to the problem (SPSQEP) are presented, and then the notions of Levitin-Polyak well-posedness and generalized Levitin-Polyak well-posedness for (SPSQEP) are introduced. Moreover, some metric characterizations of these well-posedness are derived under quite mild conditions. The relationships between these well-posedness of (SPSQEP) and the existence and uniqueness of its solutions are established. Finally, some examples are given to illustrate the presented results.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 337-355.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706390

Digital Object Identifier
doi:10.11650/tjm.18.2014.3495

Mathematical Reviews number (MathSciNet)
MR3188507

Zentralblatt MATH identifier
1357.49030

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 49K40: Sensitivity, stability, well-posedness [See also 90C31] 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)

Keywords
system of parametric strong set-valued quasi-equilibrium problem Levitin-Polyak well-posedness generalized Levitin-Polyak well-posedness Hausdorff metric Kuratowski measure of noncompactness

Citation

Chen, Jia-wei; Liou, Yeong-Cheng. SYSTEMS OF PARAMETRIC STRONG QUASI-EQUILIBRIUM PROBLEMS: EXISTENCE AND WELL-POSEDNESS ASPECTS. Taiwanese J. Math. 18 (2014), no. 2, 337--355. doi:10.11650/tjm.18.2014.3495. https://projecteuclid.org/euclid.twjm/1499706390


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