{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T17:17:37Z","timestamp":1772990257826,"version":"3.50.1"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T00:00:00Z","timestamp":1743292800000},"content-version":"vor","delay-in-days":88,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2025,1]]},"abstract":"\n Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space denoted as , where\n \u03d1<\/jats:italic>\n \u2208 {\n p<\/jats:italic>\n ,\n b<\/jats:italic>\n p<\/jats:italic>\n ,\n r<\/jats:italic>\n }, as an extension of the Hahn sequence space\n h<\/jats:italic>\n . Our investigation begins with an analysis of several topological properties of , apart from a comprehensive analysis of the relationship between Hahn double sequences and other classical double sequence spaces. The\n \u03b1<\/jats:italic>\n \u2212 dual, algebraic dual and\n \u03b2<\/jats:italic>\n (\n b<\/jats:italic>\n p<\/jats:italic>\n )\u2212 dual, and\n \u03b3<\/jats:italic>\n \u2212 dual of the space are determined. Furthermore, we define the determining set of and we state the conditions concerning the characterization of four\u2010dimensional (4D) matrix classes , where and , where . In conclusion, this research contributes to nonstandard investigation and various significant results in the space . The conducted results deepen the understanding of space and open up new avenues for further research and applications in sequence space theory.\n <\/jats:p>","DOI":"10.1155\/ijmm\/2089578","type":"journal-article","created":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T06:36:45Z","timestamp":1743316605000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Double Sequence Space H\u03d1 as an Extension of Hahn Space\n h<\/i>"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0338-3900","authenticated-orcid":false,"given":"Orhan","family":"Tu\u01e7","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9455-0326","authenticated-orcid":false,"given":"Eberhard","family":"Malkowsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4182-4458","authenticated-orcid":false,"given":"Vladimir","family":"Rako\u0107evi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3435-8417","authenticated-orcid":false,"given":"Taja","family":"Yaying","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,3,30]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01903811"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793557122502047"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.12.020"},{"key":"e_1_2_10_4_2","volume-title":"On Double Sequence and Double Series","author":"Sever Y.","year":"2006"},{"key":"e_1_2_10_5_2","volume-title":"Investigation of Double Sequence Spaces by Soft and Hard Analytical Methods","author":"Zeltser M.","year":"2001"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01696876"},{"key":"e_1_2_10_7_2","first-page":"72","article-title":"The Hahn Sequence Space","volume":"82","author":"Rao K. 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MalkowskyE. Rako\u010devi\u0107V. andYayingT. On the Double Sequence Space H\u03d1as an Extension of Hahn Space H 2024 https:\/\/arxiv.org\/abs\/2406.05117 https:\/\/doi.org\/10.48550\/arXiv.2406.05117."}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/2089578","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/ijmm\/2089578","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/2089578","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T12:17:43Z","timestamp":1772972263000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/ijmm\/2089578"}},"subtitle":[],"editor":[{"given":"Bilal","family":"Bilalov","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/ijmm\/2089578"],"URL":"https:\/\/doi.org\/10.1155\/ijmm\/2089578","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-08-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-08","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"2089578"}}