Generalized ( p , q ) $(p,q)$ -Bleimann-Butzer-Hahn operators and some approximation results

Abstract

Abstract The aim of this paper is to introduce a new generalization of Bleimann-Butzer-Hahn operators by using ( p , q ) $(p,q)$ -integers which is based on a continuously differentiable function μ on [ 0 , ∞ ) = R + $[0,\infty)=\mathbb{R}_{+}$ . We establish the Korovkin type approximation results and compute the degree of approximation by using the modulus of continuity. Moreover, we investigate the shape preserving properties of these operators.

Keywords

• ( p , q ) $(p,q)$ -integers
• ( p , q ) $(p,q)$ -Bernstein operators
• q-Bleimann-Butzer-Hahn operators
• ( p , q ) $(p,q)$ -Bleimann-Butzer-Hahn operators
• modulus of continuity
• rate of approximation