The Research About Bivariate Baskakov Type Of Operators' Approximation Property

Approximation theory which is regarded as an important branch of mathematics mainly researches that how to use some simple functions such as algebraic polynomial and trigonometric polynomial to replace or approximate the complex functions.While approximation theory of function which is seen as an important part of function theory touches upon the basic problem of the functions' approximation representation.This paper mainly research the approximation properties of the bivariate and multivariate Baskakov operators based on the existing properties of the Baskakov type's operators and the generalized Baskakov operators,it's also based on the estimation in approximation order and some researches of relative theorems,so as to enrich the existing results on the multi Baskakov operator.The organization of this dissertation is as follows.In the first chapter,we introduce briefly the origin and the progress on the function approximation theory,then we generalize the previous results about the approximation properties of the Baskakov operators,the generalized operators and the bivariate Bakakov type's operators.Finally some definitions and related notations are described used in this paper,the main content is also included.In the second chapter,we study a new multidimensional non-product-type Baskakov-Kantorovich operator by taking advantage of smoothness,so as to discuss the rate of approximation inpL spaces.In the third chapter,we give a new bivariate multiply-type Baskakov-Kantorovich operator on the basis of the Baskakov operators and get its approximation equivalent theorem on Ditizian-Totik's modulus of smoothness in Orlicz spaces.In the fourth chapter,based on the previous results of the Bernstein-Kantorovich operator and the modulus of continuity we discuss whether its deformation-Baskakov operators have the similar conclusion or not.We further prove that the Baskakov-Kantorovich operator could preserve the properties of the modulus of continuity and?AH.In the fifth chapter,we give a summary of the full article and outlook into the approximation problem of the multivariate Baskakov operators as well as its combination operators.