EQUIVALENCE THEOREM ON WEIGHTED SIMULTANEOUS L(P)-APPROXIMATION BY THE METHOD OF KANTOROVIC OPERATORS

[摘要] The aim of the present paper is to prove new direct and converse results on weighted simultaneous approximation by the method of classical Kantorovic operators in the L(p)-metric using the weighted Ditzian and Totik modulus of smoothness. We will obtain with a direct technique for integrable functions the complete equivalence characterization of weighted simultaneous approximation by this method (K-n)n epsilon N. One of the main tools and crucial estimates managing the converse and equivalence results of the simultaneous behaviour is given by a direct modified Voronovskaja theorem which uses the third order weighted modulus of smoothness. (C) 1994 Academic Press, Inc.

[发布日期] 1994-09-01