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Abstract In this paper, some qualitative approximation results for the (p,q) $(p,q)$-Bernstein operators Bp,qn(f;x) $B_{p,q}^{n}(f;x)$ are obtained for the Cauchy kernel 1x−α $\frac{1}{x-\alpha }$ with a pole α∈[0,1] $\alpha \in {}[ 0,1]$ for q>p>1 $q>p>1$. The main focus lies in the study of behavior of operators Bp,qn(f;x) $B_{p,q}^{n}(f;x)$ for the function fm(x)=1x−pmq−m $f_{m}(x)=\frac{1}{x-p^{m}q^{-m}}$, x≠pmq−m $x\neq p^{m}q^{-m}$ and fm(pmq−m)=a $f_{m}(p^{m}q ^{-m})=a$, a∈R $a\in \mathbb{R}$ and the extra parameter p provides flexibility for the approximation.