Approximation by Degenerate Hermite–Kantorovich Operators: Theory and Applications

The main objective of this article is to investigate the performance of a class of positive linear operators, namely, Kantorovich variation of Szász operators associated with degenerate Hermite polynomials for integrable functions, and their approximation characteristics are extensively investigated. The convergence of the proposed operators is proven using Korovkin‐type theorems, whereas the order of approximation is proved by classical methods and Lipschitz‐type classes. Furthermore, a bivariate extension of the operators is developed, and its uniform convergence properties, along with the associated approximation rates, are investigated. To validate the theoretical results, numerical examples are shown, and error estimates are calculated. We conclude this article by outlining future directions for this work.