Neutrosophic Approximation Theorems Via Density Ideal Method

Source abstract

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 behavior 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.