General-Appell polynomials connecting Szász-Durrmeyer type operators and their approximation properties

This manuscript presents a study on general-Appell polynomials. In this work, we construct a novel sequence of Sz$ \acute{a} $sz-Durrmeyer type operators based on general Appell polynomials to investigate approximation properties for Lebesgue integrable functions in the space $ L_1[0, \infty) $. We first establish estimates using test functions and central moments. The rate of convergence is then examined through Korovkin's theorem and a Voronovskaja-type theorem. Furthermore, we derive direct approximation results in terms of the first and second-order modulus of continuity, Peetre's K-functional, Lipschitz-type spaces, and $ r^{th} $-order Lipschitz-type maximal functions. Subsequently, we present weighted approximation results and discuss statistical approximation theorems.