After studying different forms of extending Szasz-Mirakjan operator at the interval [0,+∞) or (-∞,+∞),the author advances [AKB-] u,p (f,x) as a new form of extending Szasz-Mirakjan operator at the interval (-∞,+∞).

In this paper,the method of parabola of Bajsanski-Bojanic and the method of probability are used to study modified Szasz-Mirakjan operator L,.

Derivatives of Szász-Mirakjan operators and smoothness;

Using the moduli of smoothness w (?)λ 2 (f, t)w, direct and inverse approximation theorems with Jacobi weight of Baskakov operators is established; And the relation between derivatives of the operators and the smoothness of functions to be approximated is obtained.

In this paper we give the equivalence theorem on simultaneous approximation for combinations of Baskakov operators.

By means of DitzianTotik moduli of rorder, the local and global characterization theorems for the derivatives of the Baskakov operators are investigated.

Simultaneous approximation by Baskakov-Durrmeyer operator;

In this paper, by using the method of Bojanic,we gave an estimate on the rate of convergence of the Baskakov-Durrmeyer operator for the function of bounded variation on [0,∞) and proved that the estimate is essentially the best possible.