Approximation by the $[r]$-Baskakov sequence

We modify the classical Baskakov sequence by using a positive integer parameter $r$ to get a sequence that has a better order of approximation. We prove a convergence theorem for the modified sequence by using Korovkin’s theorem. We then give a Voronovskaya-type asymptotic theorem for this sequence. Finally, we give two examples showing that the modified sequence gives better numerical results than the classical sequence.