A new type of difference operator Δ 3 on triple sequence spaces

A New Class of Banach Sequence Spaces

New Results on the Sequence Spaces Equations Using the Operator of the First Difference

Given any sequence z = (zn)n≥1 of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y = (yn)n≥1 such that y/z = (yn/zn)n≥1 ∈ E; in particular, cz denotes the set of all sequences y such that y/z converges. By w∞, we denote the set of all sequences y such that supn≥1(n −1 ∑n k=1 |yk|) < ∞. By ∆ we denote the operator of the first difference define...

The generalized triple difference of χ sequence spaces

In this paper we define some new sequence spaces and give some topological properties of the sequence spaces χ (∆v , s, p) and Λ 3 (∆v , s, p) and investigate some inclusion relations.

On difference sequence spaces defined by Orlicz functions without convexity

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

On Some New Difference Sequence Spaces of Fractional Order

Let ∆(α) denote the fractional difference operator. In this paper, we define new difference sequence spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u). Also, the β−dual of the spaces c0(Γ, ∆(α), u) and c(Γ, ∆(α), u) are determined and calculated their Schauder basis. Furthermore, we characterize the classes (μ(Γ, ∆(α), u) : λ) for μ ∈ {c0, c} and λ ∈ {c0, c, l ∞, l1} .