一类新型Chlodovsky算子的逼近性质研究

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本文研究了一类基于非负实参数的新型Chlodovsky算子,用Ditzian-Totik光滑模与二阶连续模得到了逼近定理,然后研究了该算子对Lipschitz类函数的逼近误差上界,最后得到了该算子对一类导数为有界变差函数的绝对连续函数的收敛阶.“,”In this article,the author studies a new family of Chlodovsky operators depend-ing on a non-negative real parameter.A direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity are established.In terms of the Lipschitz class functions,an upper bound for the approximation error is obtained.Finally,the author studies the rate of convergence for some absolutely continuous functions having a derivative equivalent to a bounded variation function.
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