Rate of convergence of Szász-Durrmeyer type operators involving Hermite polynomials

This study aims to investigate a generalized version of Szász operators linked with Hermite polynomials in the Durrmeyer framework. Initially, we delve into their approximation properties employing Peetre’s K-functional, along with classical and second-order modulus of continuity. Subsequently, we evaluate the convergence speed using a Lipschitz-type function and establish a Voronovskaya-type approximation theorem. Lastly, we investigate the convergence rate for differentiable functions with bounded variation derivatives.