Abstract
In the present paper, we introduce a new band matrix and define the sequence space where is the k th Fibonacci number for every . We also establish some inclusion relations concerning this space and determine its α-, β-, γ-duals. Further, we characterize some matrix classes on the space and examine some geometric properties of this space. MSC:11B39, 46A45, 46B45, 46B20.
Highlights
Let ω be the space of all real-valued sequences
By ∞, c, c and p ( ≤ p < ∞), we denote the sets of all bounded, convergent, null sequences and p-absolutely convergent series, respectively
We say that A defines a matrix mapping from X into Y and we denote it by writing A : X → Y if for every sequence x =∞ k= ∈ X, the sequence Ax = {An(x)}∞ n=, the A-transform of x, is in Y, where
Summary
Let ω be the space of all real-valued sequences. Any vector subspace of ω is called a sequence space. Let X and Y be two sequence spaces and A = (ank) be an infinite matrix of real numbers ank, where n, k ∈ N. In , Kızmaz [ ] defined the sequence spaces
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