B-statistical core and ideal core of double sequences in 2-normed spaces via RH-regular families
AIMS Mathematics, cilt.11, sa.4, ss.9845-9875, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.3934/math.2026407
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
- Sayfa Sayıları: ss.9845-9875
- Anahtar Kelimeler: 2 normed spaces, cluster points, core, double sequences, ideal convergence, RH-regular matrices, statistical convergence
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
We investigated geometric limit sets of double sequences in finite dimensional 2-normed spaces when negligibility of index sets was measured by a density induced by a nonnegative Robison–Hamilton (RH)-regular family B of four-dimensional matrices. First, using the B-density, we defined B-statistical limit superior and limit inferior for the scalar reductions generated by the seminorms x 7→ kx, uk, and we studied the associated real cluster behavior. Next, we introduced B-statistical cluster points and the B-statistical core of a double sequence as the intersection of all closed convex sets that contained the sequence outside a B-density zero set. We obtained a disk-type representation of the core via intersections of sets of the form {x ∈ X : kx − z, uk ≤ r}, where the radii were governed by B-statistical lim sup. We also proved a Knopp-type inclusion theorem: for a family of transforms satisfying a natural B-regularity condition, the Knopp core of each transform was contained in the B-statistical core of the original sequence. Finally, replacing B-density zero sets by a strongly admissible ideal I2 on N×N, we defined ideal cores, established disk representations, compared the density-based and ideal cores, and identified an explicit condition under which the I2-core and the I∗2-core coincided.