Tikhonov regularization for a class of generalized hemivariational inequality in Banach spaces

This paper aims to study in a reflexive Banach space a class of generalized hemivariational inequality problem involving a set-valued mapping and a nonlinear perturbation. We study the solvability of the considered generalized hemivariational inequality problem and give some properties of its solutions by introducing some new coercivity conditions and hemivariational inequality property. Moreover, by means of the normalized duality mapping, we introduce the Tikhonov regularization for the problem in order to get an approximating sequence of its solutions, whose weak convergence is proved under mild conditions.