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On Domain of Nörlund Matrix

Author

Listed:
  • 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)

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 < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f 0 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.

Suggested Citation

  • Kuddusi Kayaduman & Fevzi Yaşar, 2018. "On Domain of Nörlund Matrix," Mathematics, MDPI, vol. 6(11), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:268-:d:184231
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    References listed on IDEAS

    as
    1. Mehmet Şengönül & Kuddusi Kayaduman, 2012. "On the Riesz Almost Convergent Sequences Space," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, May.
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