Deferred weighted statistical and modular convergence generated by admissible lower triangular transformations: fractional q-difference applications
AIMS Mathematics, cilt.11, sa.7, ss.23404-23436, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.3934/math.2026944
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.23404-23436
- Anahtar Kelimeler: deferred weighted statistical convergence, double sequence, fractional q-difference operator, ideal convergence, lower triangular transformation, matrix summability, Musielak–Orlicz modular convergence, strong Cesàro convergence
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
We studied deferred weighted statistical and modular convergence generated by admissible lower triangular transformations. Let A=(a_nk)_n,k≥ 0 be a triangle with nonzero diagonal entries, uniformly bounded absolute row sums, and null columns. Convergence is defined through the transformed sequence Ax along admissible deferred weighted windows. We proved that the column-null condition is equivalent to A(φ)⊆ c_0, where φ denotes the space of finitely supported sequences, and use this characterization to obtain stability under finite modifications. We established uniqueness, linearity, strong-to-statistical implications, bounded converses, Cauchy characterizations, ideal and Musielak–Orlicz extensions, and window-comparison results. Analogous results are obtained for separable transformations of double sequences. As an application, we showed that the fractional q-difference triangle Q^(q,ξ) has an ℓ_1 coefficient kernel, uniformly bounded absolute row sums, and null fixed columns. Integer orders yield banded triangles, whereas noninteger orders produce nonterminating but absolutely summable kernels.