Convergence of solutions of quasi-variational inequalities and applications

where fn : E × E → R, f : E × E → R, φn : E × E → R ∪ {∞}, φ : E × E → R ∪ {∞}. The aim of this paper is to give suitable conditions on the convergence of (fn)n to f and (φn)n to φ in order to obtain a convergence result for the solutions of (1.1)n to solutions of (1.2). This study was motivated by the increasing interest in the topic of generalized quasi-variational inequalites (in short g.q.v.i.), taking into account that a g.q.v.i. (see (3.2)) can be represented by a q.v.i. (1.2) with appropriate functions f and φ. Moreover, while the problem of the existence of solutions of q.v.i. and g.q.v.i. has been investigated in many papers (see for example [5], [6], [14]), the problem of convergence of solutions of q.v.i. has been studied, in a particular setting, only in [3]. Finally, in Section 4, we consider Nash equilibria with dependent constraints (called in [7] generalized Nash equilibrium), which can be thought