On Absolute Nörlund Spaces and Matrix Operators

New general results on matrix domains of triangles in sequence spaces

“…Then, it is easy to show that Λ(y) = ( 1/(k + 1) ) ∈ c 0 \ cs which means that y ∈ c λ 0 \ cs λ and so the inclusion cs λ ⊂ c λ 0 is strict. Finally, it is clear that Λ(e) = e ∈ ℓ ∞ \ bs which implies that e ∈ ℓ λ ∞ \ bs λ and hence the inclusion bs λ ⊂ ℓ λ ∞ is also strict which ends the proof of part (2). Moerover, part (3) is clear by combining the results of parts ( 1) and (2).…”

“…The idea of constructing a new sequence space by means of the matrix domain of a particular triangle has largely been used by several authors in different ways. For instance, see [1,2,3,4,5,6,7,9,11,13,14,17,18,19] and [20].…”

On factor relations between weighted and Nörlund means

“…A n (s) = ∞ ν=0 a nν s ν converges for n ≥ 0. Note that if A is chosen as the Nörlund matrix (r e sp.u n = n), then the summability |A, u n | k reduces to the absolute Nörlund summability N , p n , u n k [5] (r e sp. the summability N , p n k , Borwein and Cass [2]), and also N , p n 1 = N , p n , Mears [9].…”

On the new λ - sequence spaces of p - bounded variation

“…Recently, many authors in several research papers have used the idea of matrix domain to introduce new sequence spaces as the matrix domains of some particular triangles via different manners, and some of them have introduced sequence spaces of bounded variation and other types, see for instance [1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18] and [20]. In this paper, we will use the same technique to introduce the new λ-sequence spaces bv λ p of p-bounded variation and study their properties.…”