A note on a family of two-variable polynomials

AbstractThe main object of this paper is to construct a two-variable analogue of Jacobi polynomials and to give some properties of these polynomials. We show that these polynomials are orthogonal, then we obtain various recurrence formulas for them. Furthermore, we give some integral representations for these polynomials

On approximation properties of generalized Lupas type operators based on Polya distribution with Pochhammer k-symbol

The purpose of this paper is to introduce a Kantorovich variant of Lupas-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k

SOME PRESERVATION PROPERTIES OF MKZ-STANCU TYPE OPERATORS

Abstract. In this work, we construct Stancu type modification of the generalization of Meyer-König and Zeller operators (MKZ) defined i

A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials

A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials

On approximation properties of generalized Lupas type operators based on Polya distribution with Pochhammer k-symbol

The purpose of this paper is to introduce a Kantorovich variant of Lupas-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k.Kirikkale University 2020/04

On Szász-Mirakyan type operators preserving polynomials

In this paper, a modification of Szász-Mirakyan operators is studied [1] which generalizes the Szász-Mirakyan operators with the property that the linear combination $e_2 + \alpha e_1$ of the Korovkin's test functions $e_1$ and $e_2$ are reproduced for $\alpha\geq 0$. After providing some computational results, shape preserving properties of mentioned operators are obtained. Moreover, some estimations for the rate of convergence of these operators by using different type modulus of continuity are shown. Furthermore, a Voronovskaya-type formula and an approximation result for derivative of operators are calculated. Finally, some graphics which are based on our main results are shown