{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:11:15Z","timestamp":1760058675712,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council of Republic of China","award":["MOST 111-2115-M-160-002-MY2"],"award-info":[{"award-number":["MOST 111-2115-M-160-002-MY2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper mainly focuses on in-depth research on inequalities on symmetric cones. We will further analyze and discuss the inequalities we developed on the second-order cone and develop more inequalities. According to our past research in dealing with second-order cone inequalities, we derive more inequalities concerning the eigenvalue version of Young\u2019s inequality and trace a version of an inverse Young inequality and its applications. These conclusions align with the results established for the positive semidefinite cone, which is also a symmetric cone. It is of considerable help to the establishment of inequalities on symmetric cones and the analysis of their derivative algorithms.<\/jats:p>","DOI":"10.3390\/axioms14040312","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T08:24:07Z","timestamp":1744964647000},"page":"312","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Young and Inverse Young Inequalities on Euclidean Jordan Algebra"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1419-7024","authenticated-orcid":false,"given":"Chien-Hao","family":"Huang","sequence":"first","affiliation":[{"name":"General Education Center, Wenzao Ursuline University of Languages, Kaohsiung 807, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"key":"ref_1","unstructured":"Bhatia, R. (2005). 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