Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials

Abstract

In the present article, we establish a link between the theory of positive linear operators and the orthogonal polynomials by defining Bernstein-Chlodowsky-Kantorovich operators based on Gould-Hopper polynomials (orthogonal polynomials) and investigate the degree of convergence of these operators for unbounded continuous functions having a polynomial growth. In this connection, the moments of the operators are derived first, and then the approximation degree of the considered operators is established by means of the complete and the partial moduli of continuity. Next, we focus on the rate of convergence of these operators for functions in a weighted space. The associated Generalized Boolean Sum (GBS) operator of the operators under study is defined, and the degree of approximation is studied with the aid of the mixed modulus of smoothness and the Lipschitz class of Bögel continuous functions.