A generalization of Szász–Mirakyan operators based on qq-integers

In this paper, we introduce a generalization of Szász–Mirakyan operators based on qq-integers, that we call qq-Szász–Mirakyan operators. Depending on the selection of qq, 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 qq-derivatives. Furthermore, we obtain convergence properties for functions belonging to particular subspaces of C[0,∞)C[0,∞) and give some representation formulas of qq-Szász–Mirakyan operators and their rrth qq-derivatives.