Authors: Baasansuren Jadamba Akhtar A Khan Miguel Sama
Publish Date: 2011/07/08
Volume: 6, Issue: 7, Pages: 1221-1231
Abstract
This paper deals with multivalued quasi variational inequalities with pseudomonotone and monotone maps The primary objective of this work is to show that the notion of generalized solutions can be employed to investigate multivalued pseudomonotone quasi variational inequalities It is a wellknown fact that a quasi variational inequality can conveniently be posed as a fixed point problem through the socalled variational selection For pseudomonotone maps the associated variational selection is a nonconvex map and the fixed point theorems can only be applied under restrictive assumptions on the data of quasi variational inequalities On the other hand the generalized solutions are defined by posing a minimization problem which can be solved by a variant of classical Weierstrass theorem It turns out that far less restrictive assumptions on the data are needed in this case To emphasis on the strong difference between a classical solution and a generalized solution we also give a new existence theorem for quasi variational inequalities with monotone maps The main existence result is proved under a milder coercivity condition We also relax a few other conditions from the monotone map Due to its flexibility it seems that the notion of generalized solutions can be employed to study quasi variational inequalities for other classes of maps as well
Keywords: