Strong lacunary harmonic summability of fractional differences in q-rung orthopair fuzzy normed spaces
- 1Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou362000, Fujian, China
- 2Department of Mathematics, Bartin University, Bartın, Türkiye
- 3Department of Mathematics, Süleyman Demirel University, 32260Isparta, Türkiye
Abstract
We study strong lacunary harmonic summability of fractional difference sequences in q-rung orthopair fuzzy normed spaces. The fractional difference is defined on its convergence domain, with an explicit sufficient condition and a truncation estimate for bounded Banach-space-valued sequences. In the canonical norm model, the summability condition is equivalent, on bounded transformed sequences, to strong summability of the norms. We prove linearity, uniqueness and subsequence results for proper admissible ideals, and establish a transfer theorem for distinct lacunary partitions whose harmonic symmetric difference is negligible. In complete spaces, a Cauchy criterion is obtained under bounded normalized row mass; this mass bound holds automatically when β = 1. Counterexamples explain the failure of a fixed-centre zero-limit condition and the obstruction caused by unbounded row mass. The general summability results concern the transformed sequence, whereas the domain and truncation estimates use the fractional coefficients explicitly.
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BibTeX
@article{qingbo2026strong,
title = {{Strong lacunary harmonic summability of fractional differences in q-rung orthopair fuzzy normed spaces}},
author = {Cai Qing-Bo and Kişi Ömer and Gürdal Mehmet},
journal = {Demonstratio Mathematica},
year = {2026},
month = oct,
doi = {10.1515/dema-2025-0323},
url = {https://doi.org/10.1515/dema-2025-0323},
note = {CC BY},
}
RIS
TY - JOUR
TI - Strong lacunary harmonic summability of fractional differences in q-rung orthopair fuzzy normed spaces
AU - Cai Qing-Bo
AU - Kişi Ömer
AU - Gürdal Mehmet
PY - 2026
DA - 2026/10/26
JO - Demonstratio Mathematica
DO - 10.1515/dema-2025-0323
UR - https://doi.org/10.1515/dema-2025-0323
AB - We study strong lacunary harmonic summability of fractional difference sequences in q-rung orthopair fuzzy normed spaces. The fractional difference is defined on its convergence domain, with an explicit sufficient condition and a truncation estimate for bounded Banach-space-valued sequences. In the canonical norm model, the summability condition is equivalent, on bounded transformed sequences, to strong summability of the norms. We prove linearity, uniqueness and subsequence results for proper admissible ideals, and establish a transfer theorem for distinct lacunary partitions whose harmonic symmetric difference is negligible. In complete spaces, a Cauchy criterion is obtained under bounded normalized row mass; this mass bound holds automatically when β = 1. Counterexamples explain the failure of a fixed-centre zero-limit condition and the obstruction caused by unbounded row mass. The general summability results concern the transformed sequence, whereas the domain and truncation estimates use the fractional coefficients explicitly.
SN - 2391-4661
ER -