In this paper, we construct a new general class of operators which have the classical Szász Mirakyan ones as a basis, and fix the functions eax and e2ax with a> 0. The convergence of the corresponding sequences is discussed in exponential weighted spaces, and a Voronovskaya type result is given. Also we define a new weighted modulus of smoothness and determine the approximation order of the constructed operators. Finally, we study the goodness of the estimates of our new operators via saturation results.