On some new type generalized difference sequence spaces

Abstract

ABSTRACT. In this paper we introduce a new type of difference operator ∆ n m for fixed m, n ∈ N . We define the sequence spaces ∞ (∆ n m ), c(∆ n m ) and c 0 (∆ n m ) and study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces. These notions generalize many earlier existing notions on difference sequence spaces.

The spectrum of the operator $$ D( r,0, s,0,t)$$ D ( r , 0 , s , 0 , t ) over the sequence spaces $$\ell _{p}$$ ℓ p and $$bv_{p}$$ b v p

“…Let m, n ≥ 0 be fixed integers, then Esi et al [8] has introduced the following type of difference sequence spaces.…”

On generalized sequence spaces defined by modulus functions

“…[10] and [11]. Corollary 1 allows to determine F-seminorm topologies for sequence spaces from [15] and [20]. It also extends Theorem 2.6 of [9], which determines the paranorm g φ…”

“…Proposition 3 b) allows us to define alternative paranorms (or F-seminorms) in the formĝ Φ,p ν,A,v∆ m (ν ∈ {1, ∞}) on all these spaces. In addition, Corollary 3 and Proposition 3 b) determine F-seminorm (or paranorm) topologies on the spaces of type ∞ [A, v∆ m , Φ, p, X] from the papers [1], [2], [4], [8], [20], [21], [22], [24], and [43].…”

“…For example, the authors of [1], [21], and [22] [2], [3], [4], [8], [20], [24], [43], and [48] are topologized, as in Corollaries 3 and 4, by the paranorms g Φ,p ν,A,v∆ m (x) (ν ∈ {∞, 1}). Proposition 3 b) allows us to define alternative paranorms (or F-seminorms) in the formĝ Φ,p ν,A,v∆ m (ν ∈ {1, ∞}) on all these spaces.…”

Matrix transformations of Norlund–Orlicz difference sequence spaces of nonabsolute type and their Toeplitz duals

“…which are the complete spaces (see [5,27]). Kızmaz [8] gave the concept of the spaces ∞ ( ), c( ), and c 0 ( ) by using difference operator, and it was additionally summed up by Et and Çolak [6].…”