{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:26:50Z","timestamp":1760059610598,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we investigate the 3D additive-type functional equation. Next, we introduce the ternary hom-multiplier in ternary Banach algebras using the concepts of ternary homomorphisms and ternary multipliers. We first establish proof that solutions to the 3D additive-type functional equation are additive mappings. We further demonstrate that these solutions are C-linear mappings. The final portion of our work examines both the stability and hyperstability properties of the 3D additive-type functional equation, ternary hom-multiplier, and ternary Jordan hom-multiplier on ternary Banach algebras. Our analysis employs the fixed-point theorem using control functions developed by G\u01cevruta and Rassias.<\/jats:p>","DOI":"10.3390\/axioms14070494","type":"journal-article","created":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T05:53:13Z","timestamp":1750917193000},"page":"494","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability and Hyperstability of Ternary Hom-Multiplier on Ternary Banach Algebra"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3761-3535","authenticated-orcid":false,"given":"Vahid","family":"Keshavarz","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75918, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6949-4334","authenticated-orcid":false,"given":"Mohammad Taghi","family":"Heydari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75918, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3069-2816","authenticated-orcid":false,"given":"Douglas R.","family":"Anderson","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Concordia College, Moorhead, MN 56562, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"key":"ref_1","unstructured":"Ulam, S.M. 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