TheaimofthepresentpaperistoprovenewequivalenceresultsandL_p-staurationresultsonweightedsimultaneousapproximationbythemethodofBernstein-Durrmeyeroperators(includ-ingresultsin[7]).OneofthemaintoolsandcrucialestimatesmanagingtheconverseresultsisgivenbyadirectmodifiedVornorskajatheoremwhichusesthethirdorderweightedmodulusofsmoothness.