Finitely convergent iterative methods with overrelaxations revisited

We study the finite convergence of iterative methods for solving convex feasibility problems. Our key assumptions are that interior solution set is nonempty and certain overrelaxation parameters converge to zero, but with a rate slower than any geometric sequence. Unlike other works in this area, which require divergent series overrelaxations, our approach allows us consider some summable series. By employing quasi-Fejérian analysis latter case, we obtain additional asymptotic guarantees, even when empty.