A generalization of Phillips operators by using the Appell polynomials of class $A^{(2)}$

The current paper discusses some important approximation properties of a new modification of the Phillips operators with the help of $A^{(2)}$ class Appell polynomials. Firstly, we present the convergence rate of our new operators by using modulus of continuity. Then we establish a quantitative Voronovskaya-type asymptotic result. We also introduce Hermite polynomials and Gould–Hopper polynomials, which are more specific examples of Appell polynomials.