On the Rate of Convergence by Generalized Baskakov Operators

Abstract EN

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 = ∞ .