Approximation by the $[r]$-Baskakov sequence
Applicationes Mathematicae
MSC: Primary 41A25; Secondary 41A36
DOI: 10.4064/am2538-10-2024
Published online: 4 November 2024
Abstract
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.
