Deferred weighted statistical and modular convergence generated by admissible lower triangular transformations: fractional q-difference applications
AIMS Mathematics, vol.11, no.7, pp.23404-23436, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 7
- Publication Date: 2026
- Doi Number: 10.3934/math.2026944
- Journal Name: AIMS Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.23404-23436
- Keywords: deferred weighted statistical convergence, double sequence, fractional q-difference operator, ideal convergence, lower triangular transformation, matrix summability, Musielak–Orlicz modular convergence, strong Cesàro convergence
- Open Archive Collection: AVESIS Open Access Collection
- Süleyman Demirel University Affiliated: Yes
Abstract
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.