Approximation operators explored through the lens of degenerate hermite polynomials

The primary aim of this article is to present a series of positive linear operators utilizing degenerate Hermite polynomials. We explore the approximation properties for functions within diverse spaces and evaluate the order of approximation for these operators. The asymptotic behavior of the operators is scrutinized, and we establish the quantitative aspects of the asymptotic formula, accompanied by the proof of a theorem akin to Voronovskaja’s. Ultimately, we support the approximation outcomes through visual representations.