New triangular q−Fibonacci matrix

Abstract

In this study, we construct a new triangular q−analogue of the q−Fibonacci matrix˜fq =( fnk (q)) defined by ⎧ ⎪⎨ fnk (q) = ⎪⎩ qk fk (q), 1 ≤ k ≤ n fn+2 (q) − 1 0, otherwise. After, we use the analogue to define the sequence spaces c(f˜q), c0 (f˜q), ℓ∞ (f˜q), ℓp (f˜q)(1 ≤ p < ∞). Then, we provide some inclusion relations for these spaces and examine a few topological characteristics. Furthermore, we construct a basis for the space ℓp (f˜q), calculate α−, β−, γ−duals of the same space, characterize certain matrix classes, and look at some geometric properties. © 2025, University of Nis. All rights reserved.