The generalization of some theorems of P. P. Korovkin on positive operators

We introduce a class of linear operators, containing the positive operators, in which P. P. Korovkin's theorem on the conditions and order of convergence of positive operators hold. We consider also the class of linear operators, convergent to the derivative, in which similar theorems hold.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 785–794, June, 1973.