A new construction of Szasz-Mirakyan operators

The paper aims to study a generalization of Szasz-Mirakyan-type operators such that their construction depends on a function rho by using two sequences of functions. To show how the function rho play a crucial role in the design of the operator, we reconstruct the mentioned operators which preserve exactly two test functions from the set . We show that these operators provide weighted uniform approximation over unbounded interval. We establish the degree of approximation in terms of a weighted moduli of smoothness associated with the function rho. Also a Voronovskaya type result is presented. Finally some graphical examples of the mentioned operators are given. Our results show that mentioned operators are sensitive or flexible to point of wive of the rate of convergence to f, depending on our selection of rho.