A basic problem of $(p,q)$ -Bernstein-type operators.

In this note, we give an elaboration of a basic problem on convergence theorem of $(p, q)$ -analogue of Bernstein-type operators. By some classical analysis techniques, we derive an exact class of $(p_{n},q_{n})$ -integer satisfying $\lim _{n\to\infty }[n]_{p_{n},q_{n}}=\infty$ with $\lim _{n\to\infty}p_{n}=1$ and $\lim _{n\to\infty}q_{n}=1$ under $0< q_{n}< p_{n}\leq1$ . Our results provide an erratum to corresponding results on $(p,q)$ -analogue of Bernstein-type operators that appeared in recent literature. [ABSTRACT FROM AUTHOR]