Search

In this paper, we introduce a new kind of Kantorovich-type Bernstein–Stancu–Schurer operators based on the concept of ( p, q )-integers. We investigate statistical approximation properties and establish a local approximation theorem, we also give a convergence theorem for the Lipschitz continuous functions. Finally, we give some graphics and numerical examples to illustrate the convergence properties of operators to some functions. [ABSTRACT FROM AUTHOR]

In the present paper, we give an operator with the help of a generalization of Boas–Buck type polynomials by means of Gamma function. We have approximation properties and moments. The rate of convergence is given by the Ditzian–Totik first order modulus of smoothness and the K-functional. Furthermore, we obtain the point-wise estimations for this operator. [ABSTRACT FROM AUTHOR]

In the present paper, Kantorovich type λ -Bernstein operators via (p, q)-calculus are constructed, and the first and second moments and central moments of these operators are estimated in order to achieve our main results. An A-statistical convergence theorem and the rate of A-statistical convergence theorems are obtained according to some analysis methods and the definitions of A-statistical convergence, the rate of A-statistical convergence and modulus of smoothness. [ABSTRACT FROM AUTHOR]

In this paper, we introduce (p , q) -gamma operators which preserve x 2 , we estimate the moments of these operators, and establish direct and local approximation theorems of these operators. Then two approximation theorems about Lipschitz functions are obtained. The estimates on the rate of convergence and some weighted approximation theorems of the operators are also obtained. Furthermore, the Voronovskaja-type asymptotic formula is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter λ∈[−1,1]. We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness. Finally, we combine the Bojanic-Cheng decomposition method with some analysis techniques to derive an asymptotic estimate on the rate of convergence for some absolutely continuous functions. [ABSTRACT FROM AUTHOR]