The Approximation Of Generalized Baskakov Operators And Their Modified Operators

In this paper, the approximation properties about the generalized Baskakov operators and their modified operators are discussed. The paper is divided into four chapters , the contents are following:In the first chapter, the approximation properties of the generalized Baskakov operators are discussed. Absorbing the idea of the reference [3] and based on paper [2], the approximation theories of the global and pointwise of r+s order derivatives are obtained in the first part; in the second part , the inequality of Stechkin-Marchaud type of generalized Baskakov is studied.In the second chapter, the approximation theories of modified Baskakov-Beta operators are investigated. Firstly, the Voronovskaja type formula of asymptotic expansion of this kind of operators is given. Then the approximation of the bounded variation functions by the kinds of operators is discussed.In the third chapter, a kind of integral-type Baskakov operators is given . In the first part, the simultaneous approximation of this kindof operators is studied; In the second part the approximation in C [0, )of their linear combination is discussed. Absorbing the method of paper [20], the inverse theorem of a new kind of linear combination operators is obtained in the third part. In the final part, the saturation theoremof this kind of linear combination operators in C [0, ) is discussed.In the forth chapter, a necessary and sufficient condition of the approximation by the partial sum of the generalized Baskakov operators is discussed.