Well-posedness for general parametric quasi-variational inclusion problems

Abstract

In this paper, we aim to suggest the new concept of well-posedness for the general parametric quasi-variational inclusion problems (QVIP). The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for QVIP. Some metric characterizations of well-posedness for QVIP are given. We prove that under suitable conditions, the well-posedness is equivalent to the existence of uniqueness of solutions. As applications, we obtain immediately some results of well-posedness for the parametric quasi-variational inclusion problems, parametric vector quasi-equilibrium problems and parametric quasi-equilibrium problems.

Keywords:

• General parametric quasi-variational inclusion problem
• well-posedness
• approximating solution sequence
• metric characterization

Acknowledgements

The authors are thankful to the reviewers for carefully reading the paper and for pertinent comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors were partially supported by the Thailand Research Fund [grant number PHD /0078/2554] and Naresuan University. The second author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2014.44].