On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions

Abstract

In this article, we established some solution existence theorems for implicit quasivariational inequalities. We first established some results in finite-dimensional spaces and then a solution existence result in infinite-dimensional spaces was derived. Our theorems are proved for discontinuous mappings and sets which may be unbounded. The results presented in this article are improvements of results in Cubiotti, and Yao (Cubiotti, P. and Yao, J.C., 1997, Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings. Mathematical Methods of Operations Research, 46, 213–328; Cubiotti, P. and Yao, J.C., 2007, Discontinuous implicit generalized quasi-variational inequalities in Banach spaces. Journal of Global Optimization (To appear))

†On leave from the National University of Civil Engineering, 55 Giai Phong, Hanoi, Vietnam.

Keywords:

• Implicit quasivariational inequality
• Generalized quasivariational inequality
• upper semicontinuity
• Lower semicontinuity
• Hausdorff upper semicontinuity
• Hausdorff lower semicontinuity

Mathematics Subject Classi.cations 2000::

• 49J53
• 47N10
• 47J20

Acknowledgements

The authors would like to express their sincere gratitude to the referees for many helpful comments and suggestions. This research was partially supported by a grant from the National Science Council of Taiwan, R.O.C.

Notes

†On leave from the National University of Civil Engineering, 55 Giai Phong, Hanoi, Vietnam.