On the Rate of Convergence by Generalized Baskakov Operators - Yi Gao; Wenshuai Wang; Shigang Yue (Advances in Mathematical Physics)
We firstly construct generalized Baskakov operators Vn,α,q(f;x) and their truncated sum Bn,α,q(f;γn,x). Secondly, we study the pointwise convergence and the uniform convergence of the operators Vn,α,q(f;x), respectively, and estimate that the rate of convergence by the operators Vn,α,q(f;x) is 1/nq/2. Finally, we study the convergence by the truncated operators Bn,α,q(f;γn,x) and state that the finite truncated sum Bn,α,q(f;γn,x) can replace the operators Vn,α,q(f;x) in the computational point of view provided that limn→∞nγn=∞.