| Summary: | In 1978, the domain of the Nörlund matrix on the classical sequence spaces <i>l<sub>p</sub></i> and <i>l</i><sub>∞</sub> was introduced by Wang, where 1 ≤ <i>p</i> < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces <i>f</i><sub>0</sub> and <i>f</i> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>b</mi> <mi>s</mi> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mi>t</mi> </msup> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>c</mi> <mi>s</mi> <mo stretchy="false">(</mo> <msup> <mi>N</mi> <mi>t</mi> </msup> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> and examined the domain of the Nörlund mean on the <i>bs</i> and <i>cs</i>, 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 <i>α</i>-, <i>β</i>-, <i>γ</i>-duals, and characterized their matrix transformations on this space and into this space.
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