A new class of history-dependent quasi variational–hemivariational inequalities with constraints

In this paper we consider an abstract class of time-dependent quasi variational–hemivariational inequalities which involves history-dependent operators and a set unilateral constraints. First, establish the existence uniqueness solution by using recent result for elliptic in reflexive Banach spaces combined with fixed-point principle operators. Then, apply to show unique weak solvability quasistatic viscoelastic frictional contact problem. The law Signorini-type condition normal velocity nonmonotone damped response while friction is version Coulomb dry bound depends on accumulated slip.