{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T05:22:12Z","timestamp":1780464132094,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Hafr Albatin","award":["University of Hafr Albatin"],"award-info":[{"award-number":["University of Hafr Albatin"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>As a generalization of a geodesic function, this paper introduces the notion of the geodesic \u03c6E-convex function. Some properties of the \u03c6E-convex function and geodesic \u03c6E-convex function are established. The concepts of a geodesic \u03c6E-convex set and \u03c6E-epigraph are also given. The characterization of geodesic \u03c6E-convex functions in terms of their \u03c6E-epigraphs, are also obtained.<\/jats:p>","DOI":"10.3390\/axioms12040319","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T03:16:46Z","timestamp":1679627806000},"page":"319","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["New Generalization of Geodesic Convex Function"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6888-6413","authenticated-orcid":false,"given":"Ohud Bulayhan","family":"Almutairi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wedad","family":"Saleh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taibah University, Al-Medina 20012, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bolty nski, V., Martini, H., and Soltan, P.S. 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