Analyzing the Limit Set of Rough Ideal λγ-Statistical Convergence of Order α in Lattice-Valued Fuzzy Normed Spaces
Boletim da Sociedade Paranaense de Matematica, vol.44, no.7, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 7
- Publication Date: 2026
- Doi Number: 10.5269/bspm.80644
- Journal Name: Boletim da Sociedade Paranaense de Matematica
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Keywords: convexity, ideal convergence, Lattice-valued fuzzy normed space (L-fuzzy norm), limit set analysis, order of convergence (ϱ)), rough convergence, λγ-statistical convergence
- Süleyman Demirel University Affiliated: Yes
Abstract
This study introduces the framework of rough I-λγ-sstatistical convergence of order ϱ within the setting of L-fuzzy normed spaces (lattice-valued fuzzy normed spaces). This generalizes existing convergence notions by integrating ideal convergence (I), generalized sequence transformations (λγ), an arbitrary order (ϱ), and the concept of roughness (r). A primary focus is the characterization of the resulting rough limit set. We rigorously establish that, contrary to classical convergence, the limit is inherently a set. Furthermore, we prove that this limit set possesses key structural properties, specifically closure and convexity, under the topology induced by the L-fuzzy norm. Finally, we define the corresponding notion of I-λγ-statistical cluster points of order ϱ and elucidate the relationship between this set of cluster points and the rough limit set.