{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T18:45:16Z","timestamp":1767206716981,"version":"build-2238731810"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present article presents a system of symmetric equations defining multi-cubic mappings (M-CMs). Next, we describe how these mappings are structured and obtain an equation for describing them. Moreover, we Address the Hyers-Ulam stability (H-UStab) in the sense of G\u0103vru\u0163a for a symmetric multi-cubic equation through the application of the so-called Hyers (direct) method in the setting of 2-Banach spaces. For a typical case, by means of a norm, induced from a 2-norm of Rd, we examine the stability and hyperstability of a mapping f:Rdn\u27f6Rd by using a fixed point (FP) result.<\/jats:p>","DOI":"10.3390\/sym17040475","type":"journal-article","created":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T09:09:07Z","timestamp":1742548147000},"page":"475","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Approximate Multi-Cubic Mappings in 2-Banach Spaces"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4955-0842","authenticated-orcid":false,"given":"El-sayed","family":"El-hady","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1250-5014","authenticated-orcid":false,"given":"Ghazyiah","family":"Alsahli","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}]},{"given":"Abasalt","family":"Bodaghi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran 8683114676, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5348-1333","authenticated-orcid":false,"given":"Mehdi","family":"Dehghanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"ref_1","unstructured":"Ulam, S.M. (1964). Problems in Modern Mathematics, Wiley. 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Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s11784-019-0738-3","article-title":"A fixed point application for the stability and hyperstability of multi-Jensen-quadratic mappings","volume":"22","author":"Salimi","year":"2020","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"415053","DOI":"10.1155\/2013\/415053","article-title":"Solution and stability of the multiquadratic functional equation","volume":"2013","author":"Zhao","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Brzd\u0119k, J., Popa, D., Ra\u015fa, I., and Xu, B. (2018). Ulam Stability of Operators, Academic Press.","DOI":"10.1007\/978-3-030-28972-0"},{"key":"ref_12","first-page":"63","article-title":"Solution of the Ulam stability problem for cubic mappings","volume":"36","author":"Rassias","year":"2001","journal-title":"Glasnik Matematicki. 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Berichte"}],"updated-by":[{"DOI":"10.3390\/sym17060909","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000}}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/475\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T14:50:15Z","timestamp":1754232615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,21]]},"references-count":33,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["sym17040475"],"URL":"https:\/\/doi.org\/10.3390\/sym17040475","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,21]]}}}