It has already been demonstrated that a linear structure is not the unique way that gives us the opportunity to approximate a given function. By replacing sum with maximum in the linear case, max-product kind operators have been defined and this is the starting point of nonlinear approximation. Many linear operators have been examined from this perspective, and some approximation properties of them have been obtained. Here, our aim is to generalize the nonlinear Favard-Szász-Mirakjan operators via q-calculus, utilising a Shisha-Mond type theorem. Furthermore, we show that error estimates can be obtained better for some subclasses of functions.