On asymptotically lacunary statistical equivalent (Wijsman sense) set sequences via ideal and modulus function

Abstract

For any non-trivial ideal \(\mathcal{I}\) ⊆ ℘(\(\mathbb{N}\)), and any non-empty closed subset A_k ⊆ X, where (X, ρ) is a metric space. Let f be a modulus function.  The objective of this paper is to introduce and study the new notation by using a modulus function, \(\mathcal{I}\)(W_L), \(\mathcal{I}\)(fW ), \(\mathcal{I}\)[W N]\(_{θ}^{L}\), \(\mathcal{I}\)(W f^L), \(\mathcal{I}\)(\(_{θ}^{W}\) f), \(\mathcal{I}\)(W S^L) and \(\mathcal{I}\)(W S\(_{θ}^{L}\)).  Which are natural combinations of the definitions for asymptotically lacunary equivalent (Wijsman sense).  In addition, some relations among these new notions are also obtained.