Abstract
In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space b s ( N t ) and c s ( N t ) and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α-, β-, γ-duals, and characterized their matrix transformations on this space and into this space.
Highlights
Two new sequence spaces are constructed using the domain of the Nörlund matrix on the bs and cs sequence spaces. These spaces are bs( N t ) and cs( N t ), where N t is the Nörlund matrix according to t =
The necessary conditions for matrix transformations on and into these spaces are provided. They are in the form of (bs( N t ), λ), (cs( N t ), λ), (μ, bs( N t )), and (μ, cs( N t )), where we denote the class of infinite matrices moved from sequences of μ space to sequences of λ space with (μ,λ)
We detected that both spaces have the α, β, and γ-duals and calculated them
Summary
In the studies on the sequence space, creating a new sequence space and research on its properties have been important. One way to create a new sequence space in addition to standard sequence space is to use the domain of infinite matrices. Wang [2] constructed a new sequence space using an infinite matrix, unlike the infinite matrix used by Ng-Lee. In the same year, Wang [2] constructed a new sequence space using an infinite matrix, unlike the infinite matrix used by Ng-Lee These studies have been followed by many researchers such as Malkovsky [3], Altay, and Başar [4]. This topic was first studied in the 1970s but rather intensively after 2000
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