{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:03Z","timestamp":1760148303194,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T00:00:00Z","timestamp":1682035200000},"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 apply a new class of fuzzy control functions to approximate a Cauchy additive mapping in fuzzy Banach space (FBS). Further, considering the unital FBS (UFBS), we will investigate the isomorphisms defined in this space. By introducing several specific functions and choosing the optimal control function from among these functions, we evaluate the Cauchy\u2013Optimal stability (C\u2013O-stability) for all defined mappings.<\/jats:p>","DOI":"10.3390\/axioms12040405","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T06:54:19Z","timestamp":1682060059000},"page":"405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Cauchy\u2013Optimal Stability Results for Cauchy\u2013Jensen Additive Mappings in the Fuzzy Banach Space and the Unital Fuzzy Banach Space"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2517-3365","authenticated-orcid":false,"given":"Zahra","family":"Eidinejad","sequence":"first","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6770-6951","authenticated-orcid":false,"given":"Reza","family":"Saadati","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,21]]},"reference":[{"key":"ref_1","unstructured":"Ulam, S.M. 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