Error Estimation for Shifted q-Szász–Kantorovich Operators and Their Numerical Properties

This paper introduces a novel class of q-Szász–Mirakjan–Kantorovich operators defined with shifted sequences. Utilizing the basic principles of q-calculus, we design the King-type fundamental construction of q-Szász–Mirakjan–Kantorovich operators and derive their moments and central moments. The approximation properties are rigorously analyzed within the space of continuous functions. We establish the rate of convergence by employing the modulus of continuity and the integral modulus of continuity. Furthermore, we provide graphical illustrations to demonstrate the convergence behavior and efficiency of the proposed operators. Our results extend and generalize several existing findings in the field of quantum approximation theory.