A generalization of Szász–Mirakyan operators based on -integers

In this paper, we introduce a generalization of Szász–Mirakyan operators based on q -integers, that we call q -Szász–Mirakyan operators. Depending on the selection of q , these operators are more flexible than the classical Szász–Mirakyan operators while retaining their approximation properties. For these operators, we give a Voronovskaya-type theorem related to q -derivatives. Furthermore, we obtain convergence properties for functions belonging to particular subspaces of C [ 0 , ∞ ) and give some representation formulas of q -Szász–Mirakyan operators and their r th q -derivatives.