Convergence of a generalized penalty and regularization method for quasi–variational–hemivariational inequalities

In the paper an elliptic quasi–variational–hemivariational inequality with constraints in a Banach space is studied. First, we apply Minty technique, KKM principle and theory of nonsmooth analysis to establish solvability problem. Then, employ generalized penalty regularization method for introduce family penalized regularized problems no Gâteaux differentiable potentials. Through limit procedure, prove that Kuratowski upper respect weak topology solution sets problems, nonempty subset set original Next, if set-valued operator has (S)+-property, then limits strong topologies coincide. Finally, illustrate our results by examining nonlinear inclusion subgradient term locally Lipschitz function, mixed boundary conditions obstacle unilateral constraint which appears semipermeability