Serhan Varma

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.

Generalization of Szasz operators involving Brenke type polynomials

The purpose of this paper is to give a generalization of Szasz operators defined by means of the Brenke type polynomials. We obtain convergence properties of our operators with the help of Korovkins theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetres K-functional. An explicit example with our operators including Gould-Hopper polynomials which generalize Szasz operators in a natural way is given.

On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

On an inverse problem for a linear combination of orthogonal polynomials

This paper deals with the analysis of the orthogonality of a monic polynomial sequence defined as a linear combination of a sequence of monic orthogonal polynomials withwhere for . Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials . We obtain the connection between the Jacobi matrices associated with and , respectively, by using an LU factorization. Some special cases of the above type relation are analysed.

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.

Generalization of Jakimovski - Leviatan type Szasz operators

The purpose of this paper is to give a Stancu type generalization of Jakimovski-Leviatan type Szasz operators defined by means of the Sheffer polynomials. We obtain convergence properties of our operators with the help of Korovkin theorem and the order of approximation by using classical and second modulus of continuity. Explicit examples with our operators including Meixner polynomials and the 2-orthogonal polynomials of Laguerre type are given. We present two significant numerical mathematical algorithms as examples for the error estimation.