@article{Yu2026, 
author = {Hong-Zhen Yu and Ömer Kişi and Mehmet Gürdal and Qing-Bo Cai},
title = {B  -statistical core and ideal core of double sequences in    2-normed spaces via RH-regular families},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {9845-9875},
keywords = {double sequences, statistical convergence, cluster points, core, ideal convergence, RH-regular matrices, 2 normed spaces},
url = {https://www.sciopen.com/article/10.3934/math.2026407},
doi = {10.3934/math.2026407},
abstract = {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  ↦  ‖  x  ,  u  ‖, 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  :  ‖  x  −  z  ,  u  ‖  ≤  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              I        2   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              I        2  -core and the              I        2    ∗  -core coincided.}
}