{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:36:36Z","timestamp":1787027796098,"version":"3.56.0"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901030"],"award-info":[{"award-number":["11901030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing Municipality","doi-asserted-by":"publisher","award":["1232017"],"award-info":[{"award-number":["1232017"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012236","name":"Beijing Institute of Technology Research Fund Program for Young Scholars","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012236","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Open Research Fund of Hubei Key Laboratory of Mathematical Sciences","award":["MPL2024ORG004"],"award-info":[{"award-number":["MPL2024ORG004"]}]},{"name":"Youth Fund of Anhui Natural Science Foundation","award":["2008085QA01"],"award-info":[{"award-number":["2008085QA01"]}]},{"DOI":"10.13039\/501100009558","name":"University Natural Science Research Project of Anhui Province","doi-asserted-by":"publisher","award":["KJ2019A0107"],"award-info":[{"award-number":["KJ2019A0107"]}],"id":[{"id":"10.13039\/501100009558","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let A be a unital \u2217-algebra over the complex field C, and let \u03a8={\u03c8m}m\u2208N be a nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivation satisfies the relation \u03c8m(L1\u22c4L2\u22c4\u2026\u22c4Ln\u22121\u2022Ln)=\u2211r1+\u2026+rn=m\u03c8r1(L1)\u22c4\u2026\u22c4\u03c8rn\u22121(Ln\u22121)\u2022\u03c8rn(Ln), where L\u2022N=LN+NL\u2217 and L\u22c4N=L\u2217N+N\u2217L for all L,N,Li\u2208A with i\u2208{1,2,\u2026,n}. We demonstrate that every such higher derivation \u03a8={\u03c8m}m\u2208N is an additive higher \u2217-derivation. As an application, we use this result to characterize the structure of nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivations on a class of typical unital \u2217-algebras, including standard operator algebras and von Neumann factors. This result also generalizes several existing results, in particular those concerning nonlinear mixed bi-skew Jordan-type and skew Jordan derivations on unital \u2217-algebras.<\/jats:p>","DOI":"10.3390\/axioms15020138","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T16:09:32Z","timestamp":1770998972000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Nonlinear Mixed bi-Skew Jordan-Type and Skew Jordan Higher Derivations on \u2217-Algebras"],"prefix":"10.3390","volume":"15","author":[{"given":"Dandan","family":"Ren","sequence":"first","affiliation":[{"name":"School of Mathematics and Big Data, AnHui University of Science & Technology, Huainan 232001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, AnHui University of Science & Technology, Huainan 232001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6306-0578","authenticated-orcid":false,"given":"Xinfeng","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, AnHui University of Science & Technology, Huainan 232001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2169-0405","authenticated-orcid":false,"given":"Yujiao","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Algebraic Lie Theory and Analysis of Ministry of Education, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4211","DOI":"10.2298\/FIL2313211Z","article-title":"Nonlinear bi-skew Jordan-type derivations on \u2217-algebras","volume":"37","author":"Zhao","year":"2023","journal-title":"Filomat"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3231","DOI":"10.2298\/FIL2210231D","article-title":"Non-Linear Bi-Skew Jordan Derivations on \u2217-Algebras","volume":"36","author":"Darvish","year":"2022","journal-title":"Filomat"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5591","DOI":"10.2298\/FIL2317591A","article-title":"Nonlinear bi-skew Jordan-type derivations on factor von Neumann algebras","volume":"37","author":"Ashraf","year":"2023","journal-title":"Filomat"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5073","DOI":"10.1080\/00927872.2021.1937636","article-title":"\u2217-Jordan-type maps on C*-algebras","volume":"49","author":"Ferreira","year":"2021","journal-title":"Comm. 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