  In the present note, we give the generalization of $\alpha-$Baskakov
Durrmeyer operators depending on a real parameter $\rho$ > 0. We present the
approximation results in Korovkin and weighted Korovkin spaces. We also prove
the order of approximation, rate of approximation for these operators. In the
end, we verify our results with the help of numerical examples by using
Mathematica.
