{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T03:26:55Z","timestamp":1780111615445,"version":"3.54.0"},"reference-count":19,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T00:00:00Z","timestamp":1717372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell, and Changhee polynomials and numbers. One of the main applications of these integrals is to obtain symmetric identities for the special polynomials. In this study, we focus on a novel extension of the degenerate Fubini polynomials and on obtaining some symmetric identities for them. First, we introduce the two-variable degenerate w-torsion Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. By this representation, we derive some new symmetric identities for these polynomials, using some special p-adic integral techniques. Lastly, by using some series manipulation techniques, we obtain more identities of symmetry for the two variable degenerate w-torsion Fubini polynomials.<\/jats:p>","DOI":"10.3390\/sym16060686","type":"journal-article","created":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T10:06:01Z","timestamp":1717409161000},"page":"686","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Several Symmetric Identities of the Generalized Degenerate Fubini Polynomials by the Fermionic p-Adic Integral on Zp"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5567-7444","authenticated-orcid":false,"given":"Maryam Salem","family":"Alatawi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5717-1199","authenticated-orcid":false,"given":"Ugur","family":"Duran","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay 31200, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,3]]},"reference":[{"key":"ref_1","first-page":"288","article-title":"q-Volkenborn integration","volume":"9","author":"Kim","year":"2002","journal-title":"Russ. J. Math. Phys."},{"key":"ref_2","first-page":"5","article-title":"Two variable higher-order degenerate Fubini polynomials","volume":"21","author":"Kim","year":"2018","journal-title":"Proc. Jangjeon Math. 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Mathematics, 6.","DOI":"10.3390\/math6120300"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.12988\/ijma.2014.48261","article-title":"Some symmetric identities for h-extension of q-Euler polynomials under third dihedral group D3","volume":"8","author":"Dolgy","year":"2014","journal-title":"Int. J. Math. Anal."},{"key":"ref_7","first-page":"51","article-title":"Symmetric identities involving Carlitz\u2019s-type twisted h,q-tangent-type polynomials under S5","volume":"12","author":"Duran","year":"2016","journal-title":"J. New Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.jmaa.2006.09.027","article-title":"On the analogs of Euler numbers and polynomials associated with p-adic q-integralon Zp at q = \u22121","volume":"331","author":"Kim","year":"2007","journal-title":"J. Math. Anal. 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Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/686\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:53:02Z","timestamp":1760107982000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/686"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,3]]},"references-count":19,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["sym16060686"],"URL":"https:\/\/doi.org\/10.3390\/sym16060686","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,3]]}}}