{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T11:17:51Z","timestamp":1769253471735,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"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 study, we present a novel family of holomorphic and bi-univalent functions, denoted as E\u03a9(\u03b7,\u03b5;\u03dc). We establish the coefficient bounds for this family by utilizing the generalized telephone numbers. Additionally, we solve the Fekete\u2013Szeg\u00f6 functional for functions that belong to this family within the open unit disk. Moreover, our results have several consequences.<\/jats:p>","DOI":"10.3390\/sym15091747","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:34:12Z","timestamp":1694554452000},"page":"1747","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Coefficient Inequalities and Fekete\u2013Szeg\u00f6-Type Problems for Family of Bi-Univalent Functions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4341-6300","authenticated-orcid":false,"given":"Tariq","family":"Al-Hawary","sequence":"first","affiliation":[{"name":"Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9287-7704","authenticated-orcid":false,"given":"Ala","family":"Amourah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hasan","family":"Almutairi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Hafr Albatin, Hafr Albatin 39524, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8608-8063","authenticated-orcid":false,"given":"Basem","family":"Frasin","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/BF00247676","article-title":"The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1","volume":"32","author":"Netanyahu","year":"1969","journal-title":"Arch. 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