Convergence Analysis of Modified Szász Operators Associated with Hermite Polynomials

This paper presents a Stancu-type generalization of Szasz operators linked to Hermite polynomials. The convergence properties of these operators are discussed by utilizing Korovkin’s theorem. Additionally, the paper explores approximation theorems for these operators using various tools, including Peetre’s K-functional, classical and second-order modulus of continuity. The convergence rate for Lipschitz-type functions is estimated as well. Furthermore, the paper investigates the rate of weighted A-statistical convergence and demonstrates a Voronovskaya-type asymptotic result for these operators.