Gürhan İçöz

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.

A Kantorovich variant of a new type Bernstein–Stancu polynomials

Abstract A new generalization of Bernstein–Stancu Kantorovich type polynomials are constructed and the theorems on convergence and the degree of convergence are established. In addition r-th generalization is given.