Ukrainian Mathematical Journal

, Volume 69, Issue 11, pp 1772–1783 | Cite as

On Matrix Operators on the Series Space \( {\left|{\overline{N}}_p^{\theta}\right|}_k \)

  • R. N. Mohapatra
  • M. A. Sarıgöl

In recent years, the space \( {\left|{\overline{N}}_p^{\theta}\right|}_k \) has been generated from the set of k -absolutely convergent series k as the set of series summable by the absolute weighted method. We investigate some properties of this space, such as β -duality and the relationship with k and then show that each element in the classes \( \left(\left|{\overline{N}}_p\right|,{\left|{\overline{N}}_q^{\theta}\right|}_k\right) \) and \( \left({\left|{\overline{N}}_p^{\theta}\right|}_k,\left|{\overline{N}}_q\right|\right) \) of infinite matrices corresponds to a continuous linear operator and also characterizes these classes. Hence, in a special case, we deduce some well-known results of Sarıgöl, Bosanquet, Orhan, and Sunouchi.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • R. N. Mohapatra
    • 1
  • M. A. Sarıgöl
    • 2
  1. 1.University of Central FloridaOrlandoUSA
  2. 2.University of PamukkaleDenizliTurkey

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