Difference sequence spaces defined by a sequence of modulus functions

Abstract

In the present paper we study difference sequence spaces defined by a sequence of modulus functions and examine some topological properties of these spaces. Subjclass[2000]:40A05, 40C05, 46A45.

Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

“…If M (x) = x p , 0 < p < 1 then the modulus function M (x) is unbounded. For more details about modulus function and sequence spaces one may refer to ( [4], [6], [10], [22], [25], [26]) and references therein. The concept of statistical convergence was introduced by Steinhaus [28] and Fast [10] and later reintroduced by Schoenberg [27] independently.…”

A New Double Sequence Space m2(F,ϕ,p) Defined by a Double Sequence of Modulus Functions

“…Recently, Raj et al [21] introduced and studied the following sequence space ( , , ). Let = ( ) be a sequence of modulus functions.…”

On generalized sequence spaces defined by modulus functions

“…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.…”

“…Main theorems are applicable in the case if λ and Λ are strong summability domains of a non-negative matrix A = (a nk ). Some special cases of such spaces are considered, for example, in [1] - [4], [6] - [16], [19] - [25], [27], [28], [30], [31], [36], [38] - [41], [43], [45] and [48] - [51]). …”