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In this paper, we primarily use Stancu variants of Kantorovich-type operators to investigate the convergence and other associated properties of new Szász–Mirakjan operators. We compute the moments and central moments of the new Szász–Mirakjan operators by q-integers and propose their modified Kantorovich form. More specifically, we examine the convergence characteristics in the space of continuous functions. With the use of the modulus of continuity and the integral modulus of continuity, we determine the degree of convergence. Additionally, we obtain the Voronovskaja type theorems. To validate convergence, we conclude with a numerical example and graphical illustration of the operator sequences.
Nasiruzzaman et al. (Sat,) studied this question.