On the convergence of (p, q)-Bernstein operators of the rational functions with poles in [0,1]

Abstract

In the present paper, we obtain the approximation results of (p, q)-Bernstein operators Bⁿp,q(h; x) to a rational function for q > p > 1 and investigate convergence properties of Bⁿp,q(h; x) for the function h(x) = (x − pᵐq⁻ᵐ)⁻ⁿ with η > 2. Here, we observe that the approximation properties for the (p, q) -Bernstein operators are more precise in nature than the previously obtained results given in [23, 25].