Research On The Approximation Properties Of Meyer-k(?)nig And Zeller Operators

The function approximation theory is a mathematics subject with rich content and strong practice.It is closely related to applied mathematics and computational mathematics,and promotes the development of each other.As an important branch of function approximation theory,in the 1850 s,due to widely application of functional analysis,the operator approximation theory is playing an increasingly important role.The operator approximation theory mainly studies the approximation properties of functions by some classical operators(such as the Bernstein operators,Sz?(6sz operators,Baskakov operators and their modifications)in different spaces(such as continuous function space [(6,(7],space,Orlicz space,bounded variation space,H(?)lder space,complex space etc.).In this paper,we mainly study the convergence properties of Meyer-K(?)nig-Zeller operators in complex space and H(?)lder space,and the positive theorem of approximation to analytic functions and Lip functions by Meyer-K(?)nig-Zeller operators.The main content is summarized as follows:In the first chapter,the definition of Meyer-K(?)nig-Zeller operators and existing research results in real valued space was briefly introduced.By using K-functional and modulus of continuity,the convergence properties of Meyer-K(?)nig-Zeller operators in complex spaces are studied.In the second chapter,inspired by the method of the approximation of Meyer-K(?)nigZeller operator in real valued space,it is generalized to the complex space.Using the result of weighted approximation of the Baskakov operator,we obtain the approximation theorem of Meyer-K(?)nig-Zeller operator in complex spaces.In the third chapter,with the help of the properties of K-functional and modulus of continuity,by using the mean value theorem,we obtain the positive theorem of MeyerK(?)nig-Zeller operators in H(?)lder space.Finally,a summary is given,and the future possibility research on the Meyer-K(?)nigZeller Kantorovich operator is also discussed.