Rate of convergence for certain families of summation–integral type operators

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Abstract

In this paper, we study the rate of convergence for the iterative combinations of a certain family of linear positive operators in terms of higher-order integral modulus of smoothness. We have used the technique of linear approximating method, namely Steklov mean, to prove the main result. In the end, we propose some other sequences of linear positive operators and obtain the recurrence formulae for the central moments, Voronovskaja type asymptotic formulae and error estimations.

Keywords

Linear positive operators
Iterative combinations
Steklov mean
Modulus of smoothness

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