Esra Erkuş-Duman

Statistical approximation properties of high order operators constructed with the Chan–Chyan–Srivastava polynomials

Abstract In this paper, by including high order derivatives of functions being approximated, we introduce a general family of the linear positive operators constructed by means of the Chan–Chyan–Srivastava multivariable polynomials and study a Korovkin-type approximation result with the help of the concept of A -statistical convergence, where A is any non-negative regular summability matrix. We obtain a statistical approximation result for our operators, which is more applicable than the classical case. Furthermore, we study the A -statistical rates of our approximation via the classical modulus of continuity.

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.

Miscellaneous properties of some multivariable polynomials

Abstract In this paper, we present various integral representations for the Chan–Chyan–Srivastava, Lagrange–Hermite, Erkus–Srivastava multivariable polynomials and extended Jacobi polynomials. Then, we obtain some partial differential equations for the product of any two of them. We show that the Chan–Chyan–Srivastava multivariable polynomials are not orthogonal. We also discuss other miscellaneous properties of the Chan–Chyan–Srivastava, Lagrange–Hermite and Erkus–Srivastava multivariable 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.

On the g-Jacobi Matrix Functions

In this paper, we introduce a matrix version of the generalized Jacobi (g-Jacobi) function, which is a solution of fractional Jacobi differential equation, and study its fundamental properties. We also present the fractional hypergeometric matrix function as a solution of the matrix generalization of the fractional Gauss differential equation. Some special cases are discussed.

Statistical Approximation for Stochastic Processes

Abstract In this article, we obtain strong Korovkin-type approximation theorems for stochastic processes by using the concept of A-statistical convergence from the summability theory.

Some results for a family of multivariable polynomials

In this paper, we derive various families of multilinear and multilateral generating functions for a family of multivariable polynomials. We obtain an integral representation, some recurrence relations and a partial differential equation for product of two of these multivariable polynomials.