  In this paper, we consider the equilibrium problems and also their
regularized problems under the setting of Hadamard spaces. The solution to the
regularized problem is represented in terms of resolvent operators. As an
essential machinery in the existence of an equilibrium, we first prove that the
KKM principle is attained in general Hadamard spaces without assuming the
compactness of the closed convex hull of a finite set. We construct the
proximal algorithm based on this regularization and give convergence analysis
adequately.
