On differences of linear positive operators

Abstract

In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate K-functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev functional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor's formula. The obtained results are applied for some well known linear positive operators.