@article{Weng2026, 
author = {Gui-Ying Weng and Ömer Kişi and Mehmet Gürdal and Qing-Bo Cai},
title = {Deferred weighted statistical and modular convergence generated by admissible lower triangular transformations: fractional    q-difference applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {23404-23436},
keywords = {lower triangular transformation, deferred weighted statistical convergence, matrix summability, ideal convergence, Musielak–Orlicz modular convergence, fractional q-difference operator, double sequence, strong Cesàro convergence},
url = {https://www.sciopen.com/article/10.3934/math.2026944},
doi = {10.3934/math.2026944},
abstract = {We studied deferred weighted statistical and modular convergence generated by admissible lower triangular transformations. Let    A  =  (      a          n      k            )          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    A  x 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.}
}