A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators

In the present study, a novel generalization of the Szasz-Mirakyan-Kantorovich operators is delineated. The approximation properties of the aforementioned operator are investigated. Utilising the continuity modulus and functions satisfying the Lipschitz condition, the rate of approximation of the operator is calculated. The study further involves the graphical representation of the convergence of the Szasz-Mirakyan-Kantorovich operator to selected continuous functions. The margins of error in the approximation of the function are tabulated. Subsequently, a novel generalized $q$-Szasz-Mirakyan-Kantorovich operator on $q$-integers is constructed, and the classical and statistical approximation properties of this new q-operator are studied.