{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:11:11Z","timestamp":1760127071837,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we introduce and study the behavior of the modules of the first two coefficients for the classes N\u03a3(\u03b3,\u03bb,\u03b4,\u03bc;\u03b1) and N\u03a3*(\u03b3,\u03bb,\u03b4,\u03bc;\u03b2) of normalized holomorphic and bi-univalent functions that are connected with the prestarlike functions. We determine the upper bounds for the initial Taylor\u2013Maclaurin coefficients |a2| and |a3| for the functions of each of these families, and we also point out some special cases and consequences of our main results. The study of these classes is closely connected with those of Ruscheweyh who in 1977 introduced the classes of prestarlike functions of order \u03bc using a convolution operator and the proofs of our results are based on the well-known Carath\u00e9dory\u2019s inequality for the functions with real positive part in the open unit disk. Our results generalize a few of the earlier ones obtained by Li and Wang, Murugusundaramoorthy et al., Brannan and Taha, and could be useful for those that work with the geometric function theory of one-variable functions.<\/jats:p>","DOI":"10.3390\/axioms12050453","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T02:56:51Z","timestamp":1683255411000},"page":"453","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Initial Coefficients Upper Bounds for Certain Subclasses of Bi-Prestarlike Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1867-8111","authenticated-orcid":false,"given":"Tareq","family":"Hamadneh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7650-5863","authenticated-orcid":false,"given":"Ibraheem","family":"Abu Falahah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8683-6698","authenticated-orcid":false,"given":"Yazan Alaya","family":"AL-Khassawneh","sequence":"additional","affiliation":[{"name":"Data Science and Artificial Intelligence Department, Zarqa University, Zarqa 13110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1682-7809","authenticated-orcid":false,"given":"Abdallah","family":"Al-Husban","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box 2600, Irbid 21110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5838-7365","authenticated-orcid":false,"given":"Abbas Kareem","family":"Wanas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8026-218X","authenticated-orcid":false,"given":"Teodor","family":"Bulboac\u0103","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,5]]},"reference":[{"key":"ref_1","unstructured":"Duren, P.L. (1983). Univalent Functions, Springer. 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