q-Fibonacci sequence spaces and related matrix transformations - Atabey, Koray Ibrahim; Cinar, Muhammed; Et, Mikail (Springer Heidelberg, 2023)
In this paper, we define the sequence spaces l(p)((F) over cap (q)) (1 <= p < infinity), l(infinity)(<(F)over cap>(q)), c(0)((F) over cap (q)) and c((F) over cap (q)) by using q-Fibonacci band matrix (F) over cap (q) defined by (F) over cap (q) = (F) over cap (nk) (q) = {Fn+1(q)-1/q(n)F(n)(q) , k = n - 1 Fn+2(q)-1/q(n)F(n)(q) , k = n (k, n is an element of N). 0 , otherwise We study some topological properties and give some inclusion relations for these spaces. In addition, we build a bases for the space l(p)((F) over cap (q)), compute alpha-, beta,. gamma- duals of the same space, characterize some matrix classes and examine some geometric properties.
Keywords: q-Fibonacci numbers; Band matrix; Dual spaces; Matrix transform; Banach-saks property