Pseudomonotone diagonal subdifferential operators

Let f be an equilibrium bifunction defined on the product space X x X, where X is a Banach space. If f is locally Lipschitz with respect to the second variable, for every x in X we define T_f(x) as the Clarke subdifferential of f(x,\\cdot) evaluated at x.. This multivalued operator plays a fundamental role for the reformulation of equilibrium problems as variational inequality ones.. We analyze additional conditions on f which ensure the D-maximal pseudomonotonicity and the cyclically pseudomonotonicity of T_f. Such results have consequences in terms of the characterization of the set of solutions of a subclass of pseudomonotone equilibrium problems.