Fatma Taşdelen

Szász type operators involving Charlier polynomials

Abstract The purpose of this work is to give a form of positive linear operators involving Charlier polynomials, one of the discrete orthogonal polynomials which are generalization of Szasz operators. Also, Kantorovich type generalization of these operators are given. We obtain convergence properties of our operators with the help of Korovkin’s theorem and the order of approximation by using classical modulus of continuity.

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 Korovkins theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetres -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 a multivariable extension of Jacobi matrix polynomials

The classical Jacobi matrix polynomials only for commutative matrices were first studied by Defez et al. [E. Defez, L. Jodar, A. Law. Jacobi matrix differential equation, polynomial solutions and their properties, Comput. Math. Appl. 48 (2004) 789-803]. The main aim of this paper is to construct a multivariable extension with the help of the classical Jacobi matrix polynomials (JMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented.

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 generalization of Jain's operators

In this paper, we introduce a generalization of Jains operators based on a function ?. We examine convergence properties of such operators and prove a Voronovskaya type result.

A note on a family of two-variable polynomials

The 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.

Biorthogonal matrix polynomials related to Jacobi matrix polynomials

In this paper, we define the pair of biorthogonal matrix polynomials suggested by the Jacobi matrix polynomials. Biorthogonality property, matrix generating functions and matrix recurrence relations are given.

A new family of analytic functions defined by means of Rodrigues type formula

Abstract In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also derived. Examples of some members belonging to this family of analytic functions are given and differential equations satisfied by these functions are also obtained.

A study of a family of orthogonal functions in two variables

In the present paper, we consider a family of orthogonal functions and we give some recurrence relations and generating functions. We also indicate some special cases of these functions.

A Dunkl Analogue of Operators Including Two-Variable Hermite polynomials

The aim of this paper is to introduce a Dunkl generalization of the operators including two-variable Hermite polynomials which are defined by Krech and to investigate approximating properties for these operators by means of the classical modulus of continuity, second modulus of continuity and Peetre’s K-functional.