Approximation by Certain Operators Linking the $$\alpha $$-Bernstein and the Genuine $$\alpha $$-Bernstein–Durrmeyer Operators

This paper presents a new family of operators which constitute the link between \(\alpha \)-Bernstein operators and genuine \(\alpha \)-Bernstein–Durrmeyer operators. Some approximation results, which include local approximation and error estimation in terms of the modulus of continuity are given. Finally, a quantitative Voronovskaya type theorem is established and some Gruss type inequalities are obtained.

Some approximation properties by a class of bivariate operators

WOS: 000503431300041

Some approximation properties of a Durrmeyer variant ofq-Bernstein-Schurer operators