Estimates for the differences of positive linear operators and their derivatives
Offers theoretical bounds for operator differences, but the results are incremental and specialized to a narrow class of operators.
The paper provides quantitative estimates for the differences of positive linear operators (e.g., Bernstein, Kantorovich, Durrmeyer) and their derivatives in terms of the first modulus of continuity, supported by numerical examples.
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of first modulus of continuity. In order to analyze the theoretical results in the last section we consider some numerical examples.