In this study, we introduce and analyze a Kantorovich integral modification of a generalized sequence of positive linear operators, involving an additional parameter \(\beta \) that alters the kernel structure in a non-classical way, with the classical Szász–Kantorovich operator appearing as a special case. We establish the direct and limiting convergence results for the proposed operators and obtain quantitative Voronovskaya-type estimates. Furthermore, approximation properties in Lipschitz-type space are investigated, and a Grüss Voronovskaya-type theorem is derived, highlighting the interaction behavior of the newly introduced Kantorovich operators.
