Quantitative L[sub(p)]-Results for Positive Linear Operators

The author has proved several quantitative type results for determining the rate of convergence of sequences of positive linear operators to the unit. These engage the modulus of continuity of the associated function or its derivative of certain order, and they are pointwise Korovkin type inequalities, most of them sharp. Using these inequalities, we present a big variety of general Lp (1 < p < + oo) analogs, covering most of the expected cases of the convergence of positive linear operators with rates to the unit. In the same inequality we manage to combine different Lp-norms. This treatment relies on [14].