Asymptotic formulas for generalized Baskakov‐Durrmeyer operators

Abstract

The paper deals with general Baskakov‐Durrmeyer operators containing several previous definitions as special cases. We construct a new sequence of BaskakovDurrmeyer operators depending on a parameter γ. We present a quantitative Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth‐order central moment. In addition, we studied Grü ss‐type Voronovskaya theorem. All results in this work show that our new operators are flexible and sensitive to the rate of convergence to f, depending on our selection of γ(x).