{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:00:24Z","timestamp":1770980424855,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,13]],"date-time":"2024-02-13T00:00:00Z","timestamp":1707782400000},"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>In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients |a2| and |a3| for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper.<\/jats:p>","DOI":"10.3390\/sym16020226","type":"journal-article","created":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T04:18:22Z","timestamp":1707884302000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bi-Concave Functions Connected with the Combination of the Binomial Series and the Confluent Hypergeometric Function"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4052-391X","authenticated-orcid":false,"given":"Sheza M.","family":"El-Deeb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Breaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, RO-510009 Alba Iulia, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0269-0688","authenticated-orcid":false,"given":"Luminita-Ioana","family":"Cot\u00eerl\u0103","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj-Napoca, RO-400114 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grigore Stefan","family":"S\u0103l\u0103gean","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Computer Science, Babe\u015f-Bolyai University, RO-400084 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,13]]},"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":"476","DOI":"10.4153\/CJM-1970-055-8","article-title":"Coefficient estimates for a class of star-like functions","volume":"22","author":"Brannan","year":"1970","journal-title":"Can. 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