Summation rational operators of the Jackson type

Summation rational positive operators $D_{4n-n}(x;f)$ of the Jackson type are constructed on the real axis. The corresponding approximations of continuous functions $f$ on $\mathbb R$ with coinciding finite limits $\lim_{x\to-\infty}f(x)$ and $\lim_{x\to+\infty}f(x)$ are estimated.