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, cilt.44, sa.7, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 44 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.5269/bspm.80644
- Dergi Adı: Boletim da Sociedade Paranaense de Matematica
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet
Özet
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.