一个Bernstein型插值算子的逼近阶

On the Order Approximation of an Interpolation Operator of Bernstein Type

本文讨论了一个 Bernstein 型插值算子的逼近阶,所得结果优于 O.Kis 的结果.

Let P■（x）be the Jacobi polynomials,for Qn（x）=■,we consider an interpolation operator of Bern- stein type Ln（f,x）,that based on zeros of（1-x）Q,（x） In this note we prove the following theorem. Theorem.If f（x）∈C[-1;1],then ■ where the“O”is independent on f,x and n.