On Domain of Nörlund Matrix

Kuddusi Kayaduman and Fevzi Yaşar
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Kuddusi Kayaduman: Faculty of Arts and Sciences, Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey
Fevzi Yaşar: Şehitler Mah. Cambazlar Sok. No:9, Kilis 79000, Turkey

Mathematics, 2018, vol. 6, issue 11, 1-19

Abstract: In 1978, the domain of the Nörlund matrix on the classical sequence spaces l p and l ∞ was introduced by Wang, where 1 ≤ p < ∞. Tu? and Ba?ar studied the matrix domain of Nörlund mean on the sequence spaces f 0 and f in 2016. Additionally, Tu? 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.

Keywords: nörlund mean; nörlund transforms; difference matrix; ? -, ? -, ? -duals; matrix transformations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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