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Using majorization, we give new bounds for the resolvent energy of general bipartite graphs. We also find more specific lower bounds in the particular case of trees.

We consider several versions of the barrier method for a general equilibrium problem with nonlinear constraints in a reflexive Banach space setting. We suggest weak coercivity conditions instead of (generalized) monotonicity, including one containing a perturbed barrier function, in order to entail solutions for the equilibrium problem. We obtain convergence properties of the method under mild assumptions.

In this paper we investigate the Aubin property of the solution map of a parametric equilibrium problem, by providing a connection with a suitable behaviour of the diagonal subdifferential operator associated to the equilibrium bifunction. In particular, we shed some light on the relationship between metric regularity and subregularity of the diagonal subdifferential, on one side, and some properties of the bifunction, on the other side.