The Weighted Approximation By The Generalized Baskakov Operators And Other Problems

In this paper, we discuss the weighted approximation by the generalized Baskakov operators and the estimation of their remainders, at the same time, we study the approximation by the Stancu-kantorovic operators on B_a space.The main contents are divided into three parts.Part I: in the second chapter, the estimation of the remainders of the generalized Baskakov operators are discussed, several forms about the estimation of the remainders of the generalized Baskakov operators of one variables and of two variables are obtained.Part II: in the third chapter, the pointwise approximation with Jacobi weight by the generalized Baskakov operators using two-order Ditizian-Totik modulus of smoothness and the direct and converse theorems for the pointwise approximation are given. In addition, the approximation with Jacobi weight by the linear combinations of the Baskakov operators using the r-order Ditizian-Totik modulus of smoothness is studied, the theorems of approximation are obtained.Part III: in the forth chapter, the approximation by the Stancu-Kantorovic operators on B_a space is discussed, the estimation of the approximation is given.