Approximation by a new sequence of generalized α-Sz´asz-Beta Operators

Abstract

The goal of this article is to present the Sz\'{a}sz-integral type sequences of operators using the gamma function and Hermite polynomials. We also compute certain estimates at key moments and test functions. Additionally, we go over the uniform convergence theorem, which is derived from the first-order modulus of smoothness, and the order of approximation via the Korovkin theorem. We then examine pointwise approximation results in the context of Lipschitz-type space and Peetre's K-functional, second-order modulus of smoothness. Furthermore, their convergence outcomes are examined in a weighted space.convergence outcomes are examined in a weighted space.