Domain of generalized difference operator Δ _i ³ of order three on the hahn sequence space h and matrix transformations

The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv

“…e generalized difference operator Δ 3 i of order three was defined and the spectrum of Δ 3 i on the Hahn sequence space h calculated by Malkowsky et al [7]. en, the matrix domain of Δ 3 i in Hahn sequence space h was calculated by Tug et al [8].…”

“…en, most recently, the generalized difference matrix Δ 3 i � (δ nk ) domain in Hahn sequence space h was calculated and studied by Tug et al [8]. Now, we define the following difference sequence spaces as the set of all sequences whose Δ 3 i -transforms are in the sequence spaces ℓ 1 and bv as follows:…”

Compactness of quadruple band matrix operator and geometric properties

“…Many authors have used the matrix domain of difference matrices for constructing new sequence spaces and have investigated some properties of those spaces in c 0 (∆), c(∆) and ∞ (∆) in [19], ∆c 0 (p), ∆c(p) and ∆ ∞ (p) in [1], c 0 (u, ∆, p), c(u, ∆, p) and ∞ (u, ∆, p) in [2], c 0 (∆ 2 ), c(∆ 2 ) and ∞ (∆ 2 ) in [13], c 0 (u, ∆ 2 ), c(u, ∆ 2 ) and ∞ (u, ∆ 2 ) in [26], c 0 (u, ∆ 2 , p), c(u, ∆ 2 , p) and ∞ (u, ∆ 2 , p) in [5], c 0 (∆ m ), c(∆ m ) and ∞ (∆ m ) in [14], ˆ ∞ , ĉ0 , ĉ and ˆ p in [18], c 0 (B), c(B), ∞ (B) and p (B) in [29], w p 0 (r, s), w p (r, s) and w p ∞ (r, s) in [10], c 0 (B), ∞ (B) and p (B) in [9], c 0 (Q), c(Q), ∞ (Q) and p (Q) in [6], f (Q(r, s, t, u)), f 0 (Q(r, s, t, u)) and f s(Q(r, s, t, u)) in [7]. Recently, studies on the matrix domain of generalized difference matrix ∆ 3 i have also been done some authors in [30], [31], [24], [25].…”