On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ , s ˜ = ( s m ) m = 0 ∞ , t ˜ = ( t n ) n = 0 ∞ , and u ˜ = ( u n ) n = 0 ∞ are given sequences of real numbers in the set c ∖ c 0 . In this paper, we investigate the double sequence spaces E ˜ . First, we determine some topological properties and prove several inclusion relations under some strict conditions. Then, we examine α -, β ( ϑ ) -, and γ -duals of E ˜ . Finally, we characterize some new classes of 4D matrix mappings related to our new double sequence spaces and conclude the paper with some significant consequences.

On the domain of Riesz mean in the space Ls

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

On double sequence spaces defined by an Orlicz function on a seminormed space

In this paper we introduce and study the double sequence space m''(M,?,q) by using the Orlicz function M. Also we obtain some inclusion results involving the space m''(M,?,q).

On Lacunary p-Absolutely Summable Fuzzy Real-Valued Double Sequence Space

In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (

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

In this work we introduce new spaces m2(F,ϕ,p) of double sequences defined by a double sequence of modulus functions, and we study some properties of this space.

On a New I-Convergent Double-Sequence Space

The sequence space BVσ was introduced and studied by Mursaleen (1983). In this article we introduce the sequence space 2BVσI and study some of its properties and inclusion relations.