{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:51:25Z","timestamp":1760161885035,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T00:00:00Z","timestamp":1609804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used a,c\u2208R, for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper.<\/jats:p>","DOI":"10.3390\/sym13010082","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T11:51:39Z","timestamp":1609847499000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["New Conditions for Univalence of Confluent Hypergeometric Function"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02392821","article-title":"A proof of the Bieberbach conjecture","volume":"154","year":"1985","journal-title":"Acta Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1090\/S0002-9939-1961-0143950-1","article-title":"Starlike hypergeometric functions","volume":"12","author":"Merkes","year":"1961","journal-title":"Proc. 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Geometric Theory of Analytic Functions, Casa C\u0103r\u0163ii de \u015etiin\u0163\u0103."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:07:08Z","timestamp":1760159228000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,5]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010082"],"URL":"https:\/\/doi.org\/10.3390\/sym13010082","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,5]]}}}