Neutrosophic Approximation Theorems via Density Ideal Method

In this paper, we introduce and investigate the notion of density ideal convergence for sequences of neutrosophic numbers and neutrosophic valued functions. By employing weighted density ideals and [Formula: see text]–level sets, we establish several fundamental properties of density ideal quasi-Cauchy sequences and density ideal convergent sequences in the neutrosophic setting. We further define neutrosophic positive linear operators and study their approximation behaviour via a difference density ideal method. As a principal result, we prove a Korovkin-type approximation theorem for neutrosophic valued functions of two variables under [Formula: see text]–convergence. The obtained results extend classical and statistical Korovkin approximation theorems from the fuzzy framework to the neutrosophic context and provide a more general tool for handling irregular convergence phenomena through weighted density ideals.