Weighted Approximation Of A Kind Of Baskakov Type Operators Questions

The classical Baskakov operators were first introduced by V.A.Baskakov in literature [1] in 1957, Jesus De La Cal and Francisco get a new kind of Baskakov operators by generalized it in literature [2] in 1994 and they also show the convergences are monotonic, if the involved function in convex. By means of Ditzian-Totik modulus, the Baskakov type operators and their derivatives is estimated in literature [3] by Yang ruihuan and Sun weibin in 2009. The direct theorem of weighted approximation as well as the equivalent relation between second derivatives and smoothness of the function is obtained. This literature [4] deal with the approximating problem by the classic Baskokav operator in Lp space, get the direct theorem by Jiang gongjian and Liu wencan in 1995.At this dissertation, we use the generalized Baskakov operator in literature [2] and the weighted approximation of the generalized Baskakov operator in C space in literature [3] to discuss the approximating problem by this generalized Baskakov operator in Lp space and Orlicz space.We get three theorems about generalized Baskakov operator in Lp space in chapter 2. Theorem2.1 (direct theorem):suppose f(x)∈Lp [0,∞)(1