Almost convergence and triple band matrix

On the spaces of Nörlund almost null and Nörlund almost convergent sequences

“…After computing the beta and gamma duals of f 0 and f they characterized the classes ( f : µ) and (µ : f ) of infinite matrices and they determined some core theorems related to the space f . Recently, Sönmez [18] worked the domain f (B) of the triple band matrix B(r, s, t) in the space f .…”

“…(viii) A ∈ ( ∞ (N t ) : c) if and only if (10) and (13) hold with b nk instead of a nk . (ix) A ∈ ( p (N t ) : f ) if and only if(14),(18) and(19)hold with b nk instead of a nk .…”

Absolute almost weighted summability methods

“…This notation plays an important role in summability theory, approximation theory and Fourier analysis and was investigated by several authors. For example, it was later used to define and study some concepts such as conservative and regular matrices, some sequence spaces and matrix transformations (see [2], [6], [7], [9], [10], [11], [15]).…”

Euler-Ces`aro difference spaces of bounded, convergent and null sequences

“…which is a sequence space. By using the matrix domain of a triangle matrix, so many sequence spaces have recently been defined by several authors, see for instance [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. In the literature, the matrix domain λ ∆ is called the difference sequence space whenever λ is a normed or a paranormed sequence space, where ∆ denotes the backward difference matrix ∆ = (∆ nk ) and ∆ ′ = (∆ ′ nk ) denotes the transpose of the matrix ∆, the forward difference matrix, which are defined by…”

“…for all k, n ∈ N and r, s, t ∈ R \ {0}. Also in [6,7,8,9,10,11], certain difference sequence spaces are studied. Quite recently, Başar has studied the space ℓ p of p-absolutely B-summable sequences, in [12].…”