The Generalization Of Kantorovich Operator And The Approach Problems Of Functions

The approximation operator for every kind of the objective function is different in Approximation Theory. Kantorovich operator is the generalization of the Bernstein operator. In this paper, the generalization of the Kantorovich operator , the random Kantorovich operator and the approximative problems of the new operators are discussed basing on the approximative properties of the Bernstein operator.This paper generalizes the Kantorovich operator by the weighted method. The weighted Kantorovich operator reflects the different effects and influences of the function in every part of the interval [k/(n+1),((k+1)/(n+1))]. So, there must be some different performances by changing the relevant weighted functions. And the conception of the modified Kantorovich operator is presented. Making use of this operator, the terms of the sum formula is reduced. It means that the computational amount is decreased. In addition, the new operators keep the approximative properties, too. At last, by means of some results of the random theory, the Kantorovich operator approximation theorems for random functions are given. So the Approximation Theory is enriched .