THE L_p-SATURATION RESULTS WEIGHTED SIMULTANEOUS APPROXIMATION BY THE METHOD OF BERNSTEIN-DURRMEYER OPERATORS

The aim of the present paper is to prove new equivalence results and L_p-stauration results onweighted simultaneous approximation by the method of Bernstein-Durrmeyer operators (includ-ing results in 7]). One of the main tools and crucial estimates managing the converse results isgiven by a direct modified Vornorskaja theorem which uses the third order weighted modulus ofsmoothness.