This paper investigates two fixpoint approaches for minimal model reasoning with disjunctive logic programs P. The first one, called model generation, is based on an operator T_P^INT defined on sets of Herbrand interpretations whose least fixpoint is logically equivalent to the set of minimal Herbrand models of the program. The second approach, called state generation, uses a fixpoint operation T_P^s based on hyperresolution. It operates on disjunctive Herbrand states, and its least fixpoint is the set of logical consequences of P, the so-called minimal model state of the program. We establish a useful relationship between hyperresolution by P_P^s and model generation by T_P^INT. Then we investigate the problem of continuity of the two operators T_P^s and T_P^INT. It is known that the operator T_P^s is continuous, and so it reaches its least fixpoint in at most ω iterations. On the other hand, the question of whether T_P^INT is continuous has been open. We show by a counterexample that T_P^INT is not continuous. Nevertheless, we prove that it converges towards its least fixpoint in at most ω iterations, too, as follows from the relationship that we show exists between hyperresolution and model generation. We define an iterative version of T_P^INT that computes the perfect model semantics of stratified disjunctive logic programs. On each stratum of the program, this operator converges in at most ω iterations. Model generations for the stable semantics and the partial stable semantics are respectively achieved by using this iterative operator together with the evidential transformation and the 3-S transformation.