Rabia Aktaş

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 note on parameter derivatives of the Jacobi polynomials on the triangle

The aim of the present paper is to obtain derivatives of the Jacobi polynomials with two variables on the triangle with respect to their parameters by using the parameter derivatives of the classical Jacobi polynomials P n ( α , β ) ( x ) . Furthermore, we give orthogonality properties of the parametric derivatives on the triangle.

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 new multivariable extension of Humbert matrix polynomials

The purpose of this paper is to define a matrix version of a generalization (and unification) of a class of Humbert polynomials which include many well-known multivariable polynomials and to discuss some properties such as bilateral and bilinear generating matrix functions, recurrence relations, differential equation for these generalized matrix polynomials.

On a multivariable extension of the Humbert polynomials

Abstract In this paper, we present a multivariable extension of the Humbert polynomials, which is motivated by the Chan–Chyan–Srivastava multivariable polynomials, the multivariable extension of the familiar Lagrange–Hermite polynomials and Erkus–Srivastava multivariable polynomials. We derive various families of multilinear and mixed multilateral generating functions for these polynomials. Other miscellaneous properties of these multivariable polynomials are also discussed. Some special cases of the results presented in this study are also indicated.

On parameter derivatives of a family of polynomials in two variables

The purpose of the present paper is to give the parameter derivative representations of the form ? P n , k ( λ ; x , y ) ? λ = ? m = 0 n - 1 ? j = 0 m d n , j , m P m , j ( λ ; x , y ) + ? j = 0 k e n , j , k P n , j ( λ ; x , y ) for a family of orthogonal polynomials of variables x and y, with λ being a parameter and 0 ≤ k ≤ n ; n , k = 0 , 1 , 2 , ? . First, we shall present the representations of the parameter derivatives of the generalized Gegenbauer polynomials C n ( λ , µ ) ( x ) with the help of the parameter derivatives of the classical Jacobi polynomials P n ( α , β ) ( x ) , i.e. ? ? α P n ( α , β ) ( x ) and ? ? β P n ( α , β ) ( x ) . Then, by using these derivatives, we investigate the parameter derivatives for two-variable analogues of the generalized Gegenbauer polynomials. Furthermore, we discuss orthogonality properties of the parametric derivatives of these polynomials.

The Laguerre polynomials in several variables

In this paper, we give some relations between multivariable Laguerre polynomials and other well-known multivariable polynomials. We get various families of multilinear and multilateral generating functions for these polynomials. Some special cases are also presented.

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.

On a Family of Multivariate Modified Humbert Polynomials

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials.