The convergence of $(p,q)$-Bernstein operators for the Cauchy kernel with a pole via divided difference
The convergence of $(p,q)$-Bernstein operators for the Cauchy kernel with a pole via divided difference
In this paper, some qualitative approximation results for the $(p,q)$ -Bernstein operators $B_{p,q}^{n}(f;x)$ are obtained for the Cauchy kernel $\frac{1}{x-\alpha }$ with a pole $\alpha \in {}[ 0,1]$ for $q>p>1$ . The main focus lies in the study of behavior of operators $B_{p,q}^{n}(f;x)$ for the function $f_{m}(x)=\frac{1}{x-p^{m}q^{-m}}$ , $x\neq p^{m}q^{-m}$ …