On the Rate of Convergence by Generalized Baskakov Operators

We firstly construct generalized Baskakov operators V-n,V-alpha,V-q(f;x) and their truncated sum B-n,B-alpha,B-q(f;gamma(n),x). Secondly, we study the pointwise convergence and the uniform convergence of the operatorsV(n,alpha,q)(f;x), respectively, and estimate that the rate of convergence by the operatorsV(n,alpha,q)(f;x) is 1/n(q/2). Finally, we study the convergence by the truncated operators B-n,B-alpha,B-q(f;gamma(n),x) and state that the finite truncated sum B-n,B-alpha,B-q(f;gamma(n),x) can replace the operators V-n,V-alpha,V-q(f;x) in the computational point of view provided that lim(n ->infinity) root n gamma(n) = infinity.