On the Rate of Convergence by Generalized Baskakov Operators

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. 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 lim n→∞ √nγ n = ∞.