{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:47:59Z","timestamp":1760233679866,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T00:00:00Z","timestamp":1612396800000},"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>The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach\u2019s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.<\/jats:p>","DOI":"10.3390\/sym13020259","type":"journal-article","created":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T03:15:28Z","timestamp":1612408528000},"page":"259","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Applications of Inequalities in the Complex Plane Associated with 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":[[2021,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/0022-247X(78)90181-6","article-title":"Second order differential inequalities in the complex plane","volume":"65","author":"Miller","year":"1978","journal-title":"J. Math. Anal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1307\/mmj\/1029002507","article-title":"Differential subordinations and univalent functions","volume":"28","author":"Miller","year":"1981","journal-title":"Mich. Math. J."},{"key":"ref_3","first-page":"815","article-title":"Subordinants of differential superordinations","volume":"48","author":"Miller","year":"2003","journal-title":"Complex Var."},{"key":"ref_4","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02392821","article-title":"A proof of the Bieberbach conjecture","volume":"154","author":"Branges","year":"1985","journal-title":"Acta Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0002-9939-1990-1017006-8","article-title":"Univalence of Gaussian and confluent hypergeometric functions","volume":"110","author":"Miller","year":"1990","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations. Theory and Applications, Marcel Dekker, Inc.","DOI":"10.1201\/9781482289817"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Oros, G.I. (2021). New Conditions for Univalence of Confluent Hypergeometric Function. Symmetry, 13.","DOI":"10.3390\/sym13010082"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.2478\/s12175-014-0269-8","article-title":"Subordination and superordination results associated with the generalized hypergeometric function","volume":"5","author":"Magesh","year":"2014","journal-title":"Math. Slovaca"},{"key":"ref_10","first-page":"65","article-title":"Subordination and superordination properties for analytic functions involving Wright\u2019s functions","volume":"66","author":"Murugusundaramoorthy","year":"2011","journal-title":"Le Mat."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cho, N.E., Aouf, M.K., and Srivastava, R. (2019). The principle of differential subordination and its application to analytic and p-valent functions defined by a generalized fractional differintegral operator. Symmetry, 11.","DOI":"10.3390\/sym11091083"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/259\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:19:50Z","timestamp":1760159990000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,4]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020259"],"URL":"https:\/\/doi.org\/10.3390\/sym13020259","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,2,4]]}}}