{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:13:54Z","timestamp":1775225634477,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","doi-asserted-by":"publisher","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article investigates fundamental inequalities within a golden-like statistical manifold (GLSM) equipped with a semi-symmetric metric connection (SSMC). We explore key geometric and analytical properties, including curvature relations and inequalities analogous to those in classical information geometry. The interplay between the golden-like structure and the SSMC yields new insights into the underlying differential geometric framework. Our results extend known inequalities in the statistical manifold (SM), providing a foundation for further studies in optimization and divergence theory within this generalized framework.<\/jats:p>","DOI":"10.3390\/sym17091380","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T00:09:32Z","timestamp":1756080572000},"page":"1380","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Curvature Inequalities in Golden-like Statistical Manifolds Admitting Semi-Symmetric Metric Connection"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7359-484X","authenticated-orcid":false,"given":"Foued","family":"Aloui","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5901-2511","authenticated-orcid":false,"given":"Ibrahim","family":"Al-Dayel","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0901-6123","authenticated-orcid":false,"given":"Mohammed","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad 500032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Majid Ali","family":"Choudhary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad 500032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"key":"ref_1","unstructured":"Amari, S. (2012). Differential-Geometrical Methods in Statistics, Springer Science & Business Media."},{"key":"ref_2","unstructured":"Nomizu, K., Katsumi, N., and Sasaki, T. (1994). 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