Rough I-γτ-Statistical Convergence of Order α in Neutrosophic Normed Spaces

Ahmad M., Mursaleen M., SAVAŞ E.

Journal of Intelligent and Fuzzy Systems, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1177/18758967261437338
  • Dergi Adı: Journal of Intelligent and Fuzzy Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: convex set., convexity of limit sets, I-statistical cluster points, I-statistical convergence, neutrosophic normed space, rough convergence, γτ-pstatistical convergence
  • Uşak Üniversitesi Adresli: Evet

Özet

In this paper, we investigate rough I[jls-end-space/]- γ τ[jls-end-space/]-statistical convergence of order α in neutrosophic normed spaces and establish several fundamental structural properties of the associated limit sets. We first show that the family { Lj } j ≥ 0 of rough statistical limit sets is monotone with respect to the roughness parameter j[jls-end-space/], and each Lj is convex under mild monotonicity assumptions on the neutrosophic components. For j = 0[jls-end-space/], rough convergence reduces to the classical I[jls-end-space/]- γ τ[jls-end-space/]-statistical convergence of order α[jls-end-space/], ensuring that the limit set is a singleton. We further demonstrate that the rough limit set is always neutrosophically closed and neutrosophically convex, highlighting its stability under both topological and geometric operations. A characterization of strong I[jls-end-space/]- s t γ τ α[jls-end-space/]-boundedness is obtained via the non-emptiness of the rough limit set. In addition, we introduce the notion of Ij − s t γ τ α[jls-end-space/]-cluster points and prove that every rough limit point is a cluster point, while the cluster set remains neutrosophically closed. Finally, we show that this convergence framework unifies several classical notions of statistical and ideal convergences as particular cases.