On the rate of convergence by generalized Baskakov operators

Abstract

We firstly construct generalized Baskakov operators V n, α, q (f; x) and their truncated sum B n, α, q (f; γ n, x). Secondly, we study the pointwise convergence and the uniform convergence of the operators V n, α, q (f; x), respectively, and estimate that the rate of convergence by the operators V n, α, q (f; x) is 1 / n q / 2. Finally, we study the convergence by the truncated operators B n, α, q (f; γ n, x) and state that the finite truncated sum B n, α, q (f; γ n, x) can replace the operators V n, α, q (f; x) in the computational point of view provided that l i m n → ∞ n γ n = ∞. © 2015 Yi Gao et al