Some equivalence results for well-posedness of generalized hemivariational inequalities with clarke s generalized directional derivative

In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke s generalized directional derivative in re exive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke s generalized directional derivative under different monotonicity assumptions, we establish two kinds of conditions under which the strong α -well-posedness and the weak α -well-posedness for the generalized hemivariational inequality with Clarke s generalized directional derivative are equivalent to the existence and uniqueness of its solution, respectively.