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A New Series Space Derived by Absolute Generalized Nörlund Means

  • Canan Hazar Güleç
Veröffentlicht/Copyright: 4. August 2023
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ABSTRACT

In a way different from traditional methods, recently, new series spaces have been established by using absolute summability methods. Among these absolute summability methods, the absolute generalized Nörlund summability method |N, pn, qn, θn|k is extremely important as it includes several summability methods such as absolute Nörlund, weighted, Cesàro and Euler summability methods. Now, it is natural to ask behavior of the space derived by the absolute summability of generalized Nörlund means. The purpose of this study is to derive a more general series space including some well known spaces such as the spaces |N˜qθ|k , |Cα|k, |Cα, β|k, |Npθ|k and |Erθ|k , and to investigate its topological structure, α-, β- and γ-duals. Beside this, some matrix transformations related to these spaces have been characterized.

2020 Mathematics Subject Classification: 40C05; 40D25; 40F05; 46A45

(Communicated by Gregor Dolinar)


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Received: 2021-10-07
Accepted: 2022-09-09
Published Online: 2023-08-04

© 2023 Mathematical Institute Slovak Academy of Sciences

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