We introduce modified gamma operators in polynomial weighted spaces of differentiable functions and give approximation theorems for them.

In the papers [5]-[7] was examined approximation of functions by the modified Szász-Mrakyan operators and other positive linear operators preserving e2(x) = x 2. In this paper we introduce the Post-Widder and Stancu operators preserving x 2 in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators.

ABSTRACT. We introduce certain generalized Szász-Mirakyan operators in exponential weight spaces of functions of two variables and we give approximation theorems for them.

We introduce certain modified Meyer-König and Zeller operators Mn;r in the space of r-th times differentiable functions f and we study strong differences H q n;r (f ) for them. This note is motivated by results on strong approximation connected with Fourier series ([7]).