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

Gamma Generalization Operators Involving Analytic Functions

In the present paper, we give an operator with the help of a generalization of Boas–Buck type polynomials by means of Gamma function. We have approximation properties and moments. The rate of convergence is given by the Ditzian–Totik first order modulus of smoothness and the K-functional. Furthermore, we obtain the point-wise estimations for this operator