q-Stancu算子的保形性及收敛定理

给出了基于q-整数的Stancu算子Ln（·，q），同时研究了该算子的一些基本性质．首先，利用q-Stancu算子作用于某一函数f（x）以后Ln（f，q；x）与f（x）变号数的关系，得到了该算子的保形性定理．其次，通过精细的不等式放缩，该算子作用于一般的连续函数后收敛于一极限算子，而不像一般算子那样收敛于函数本身，并用光滑模刻画了其收敛速度．

Shape-preserving and convergence properties of q-Stancu operator.

A generalization of Stancu operator based on q-integer is introduced.And some essential properties of this operator are investigated.One of these properties is the shape-preserving property which is studied with the help of the sign changes of f(x) and Ln(f,q;x).The other is the convergence property.On this aspect,q-Stancu operator behaves quite differently compared with the usual operator such as Bernstein operator,Stancu operator and so on.