A Chlodowsky variation of generalized Szász type operators and a novel sequence of operators, containing the Appell polynomials of class $\mathbb{A}^{(2)}$, are the subjects of this study. Approximation properties and convergence results are given by using different types of modulus of continuity with the help of Steklov function. A weighted space of functions constructed on $[0, +\infty)$ is used to study the convergence features of these operators. Theoretical conclusions are demonstrated by using the Gould-Hopper and Hermite polynomials.