On the Rate of Convergence by Generalized Baskakov Operators

Abstract

We firstly construct generalized Baskakov operators , , ( ; ) and their truncated sum , , ( ; , ). Secondly, we study the pointwise convergence and the uniform convergence of the operators , , ( ; ), respectively, and estimate that the rate of convergence by the operators , , ( ; ) is 1/ /2 . Finally, we study the convergence by the truncated operators , , ( ; , ) and state that the finite truncated sum , , ( ; , ) can replace the operators , , ( ; ) in the computational point of view provided that lim → ∞ √ = ∞.

Convergence Theorems for Derivatives of a New Baskakov -Type Operators

“…To approximate some real valued functions and continuous on the interval [0, ∞), Baskakov [1] Lots of researchers interested in the well known theorem (the Voronoviskaya -type theorem),and they studied the rate of convergence in weighted space, they introduced and proved them for some oeperators one of them the modifieds Baskakov operators [6] and [7].…”