In the present manuscript, we consider ?-Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, prove Voronovskaja type, quantitative type and Gr?ss-Voronovskaja asymptotic formula, rate of convergence by means modulus continuity for functions in Lipschitz space. Finally, show that numerical examples which describe validity theoretical example effectiveness de...

Abstract. We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein–Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the deriva...

Keywords: Bernstein operators Pointwise approximation Rate of convergence a b s t r a c t In the present paper, we study pointwise approximation by Bernstein–Durrmeyer type operators in the mobile interval x 2 0; 1 À 1 nþ1 h i , with use of Peetre's K-functional and x 2 u k ðf ; tÞ ð0 6 k 6 1Þ, we give its properties and obtain the direct and inverse theorems for these operators.

Khan [4] and Mishra [5] have proved some results dealing with the degree of approximation of functions in Lpspaces using different types of operators. BaskakovDurrmeyer operators were first considered by Sahai-Prasad [8] in 1985 . Sinha et al. [9] improved and corrected the results of [8]. In 2005, Finta [1], introduced a new type of Baskakov-Durrmeyer operator by taking the weight function of ...

We define GBS operators of Durrmeyer for bivariate functions on simplex and we give their approximations rate B-continuous B-differentiable functions. show that the type new have better approximation than operators.

The purpose of this paper is the investigation of strong converse results for Bernstein-Durrmeyer operators and their quasi-interpolants. For lower dimensions we improve known results by Knoop and Zhou [16] and Chen, Ditzian and Ivanov [5] in regard to the constants in their estimates and prove a strong converse theorem of type B for the quasi-interpolants introduced by Berdysheva, Jetter and S...