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On the New Hahn Sequence Space h(2).

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Title: On the New Hahn Sequence Space h(2).
Authors: Tuğ, Orhan1 (AUTHOR) orhan.tug@tiu.edu.iq, Fiorenza, Alberto1 (AUTHOR) fiorenza@unina.it
Source: Abstract & Applied Analysis. 8/7/2025, Vol. 2025, p1-8. 8p.
Subjects: Sequence spaces, Difference operators, Linear operators, Duality theory (Mathematics), Topological property
Abstract: This paper investigates the properties and structural characteristics of the new Hahn sequence space defined by using the second‐order forward difference operator. First, we introduce the new Hahn sequence space:h2=x=xl∈ω:∑l=1∞l+1 Δ2xl<∞, liml→∞xl=0, of order two. Then, we show some topological properties of this new sequence space h(2), and calculate our new Hahn sequence space's alpha‐dual, beta‐dual, and gamma‐dual. Finally, we calculate some matrix transformations from the new Hahn sequence space h(2) into the space α=l1,l∞, c,c0, lr, h and from the space β=l1,l∞, c,c0, lp, h into the new Hahn sequence space h(2). [ABSTRACT FROM AUTHOR]
Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Abstract+%26+Applied+Analysis%22&quot;&gt;Abstract &amp; Applied Analysis&lt;/searchLink&gt;. 8/7/2025, Vol. 2025, p1-8. 8p.
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  Data: &lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Sequence+spaces%22&quot;&gt;Sequence spaces&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Difference+operators%22&quot;&gt;Difference operators&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Linear+operators%22&quot;&gt;Linear operators&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Duality+theory+%28Mathematics%29%22&quot;&gt;Duality theory (Mathematics)&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Topological+property%22&quot;&gt;Topological property&lt;/searchLink&gt;
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  Data: This paper investigates the properties and structural characteristics of the new Hahn sequence space defined by using the second‐order forward difference operator. First, we introduce the new Hahn sequence space:h2=x=xl∈ω:∑l=1∞l+1 Δ2xl&lt;∞, liml→∞xl=0, of order two. Then, we show some topological properties of this new sequence space h(2), and calculate our new Hahn sequence space&#39;s alpha‐dual, beta‐dual, and gamma‐dual. Finally, we calculate some matrix transformations from the new Hahn sequence space h(2) into the space α=l1,l∞, c,c0, lr, h and from the space β=l1,l∞, c,c0, lp, h into the new Hahn sequence space h(2). [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: &lt;i&gt;Copyright of Abstract &amp; Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1155/aaa/6726703
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      – Code: eng
        Text: English
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        PageCount: 8
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    Subjects:
      – SubjectFull: Sequence spaces
        Type: general
      – SubjectFull: Difference operators
        Type: general
      – SubjectFull: Linear operators
        Type: general
      – SubjectFull: Duality theory (Mathematics)
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      – SubjectFull: Topological property
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      – TitleFull: On the New Hahn Sequence Space h(2).
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            NameFull: Tuğ, Orhan
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            NameFull: Fiorenza, Alberto
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          Dates:
            – D: 07
              M: 08
              Text: 8/7/2025
              Type: published
              Y: 2025
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              Value: 2025
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