alpha-strong approximate solutions to quasi-variational inequalities

  • Mohamed Ait Mansour Polydisciplinary faculty, Safi, Cadi Ayyad university Morocco
  • J. Lahrache Faculté des Sciences, Université Chouaib Doukkali
  • N.- E. Ziane Faculté des Sciences, Université Chouaib Doukkali


In this paper, based on the regularization of non necessarily semicontinuous set-valued maps
established in [4], we prove existence results of strong approximate solutions to quasivariational inequalities,
(QVI), without any continuity condition on its related operator. A condition ensuring the convergence
of a sequence of such solutions to an exact one is also provided. Moreover, we observe that the regularization
of [4] leads to new approximate solutions of a weak type. The latter is not in the scope of this note
as it poses a new open geometrical question on the normal cone to a subset, which we underline by the
conclusion section.