| Nesar Hossain†, Rahul Mondal‡
Abstract: In this paper, we propose the concept of ρ-strong convergence for difference sequences of fractional order, denoted by ∆α–ρ-strong convergence, in a q-rung orthopair fuzzy normed space. We establish the uniqueness of this convergence and provide its algebraic characterization. A convergence criterion for subsequences is derived, and the relationship between ∆α-strong convergence and ∆α–ρ-strong convergence is examined under conditions on lim inf sρs . Moreover, an inclusion result is obtained by employing a positive non-decreasing sequence µs satisfying ρs < µs under suitable assumptions. Finally, we introduce the notion of ρ-strongly Cauchy difference sequences of fractional order and investigate their connection with ∆α–ρ-strong convergence. Keywords: q-rung orthopair fuzzy normed space, t-norm, t-conorm, ∆α–ρ-strong convergence, ∆α–ρ-strong Cauchy sequence. MSC: 40A05, 03E72, 46A45, 40C05. DOI 10.56082/annalsarscimath.2026.2.43 †nesarhossain24@gmail.com, Department of Basic Science and Humanities, Dumkal Institute of Engineering and Technology, West Bengal 742406, India |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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