L p -Korovkin Type Inequalities for Positive Linear Operators

Abstract

The author, in recent years, has produced several quantitative type of results for estimating the rate of convergence of a sequence of positive linear operators to the unit. These involve the modulus of continuity of the associated function or its derivative of certain order, and they are pointwise Korovkin type inequalities, most of them shaTp. Using these inequalities, we are able to produce a great variety of general L1' (1 ::; )I ::; +00) analogs, covering most of the expected cases of the convergence of positive linear operators with rates to the unit. In the same inequality we achieve to combine different Lp-norms.