The Voronovskaja type expansion fomula of the modified Baskakov-Beta operators;

By using the probability theory,the pointwise approximations for bounded variation functions of the modified Baskakov-Beta operators are studied.

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.

Simultaneous approximation by Baskakov operators;

Pointwise direct and converse estimates for Baskakov operators;

Two kinds of preserved porperty by modified Baskakov operator;

Using some results and methods of probability theory and Abel transformation,the paper has studied the approximation of a Baskakov type operators whose limits are Gamma operator for functions of bounded variation of order p,and the pointwise convergence theorem of these operstors are obtained.

Pointwise Approximation Properties for the Derivatives of Baskakov-Kantorovich Operators;

The relation between higher order derivatives of Baskakov-Kantorovich operators and the smoothness of the functions to be approximated is studied.