{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T09:06:01Z","timestamp":1775379961947,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T00:00:00Z","timestamp":1677024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Umm Al-Qura University","award":["22UQU4330056DSR01"],"award-info":[{"award-number":["22UQU4330056DSR01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in the symmetry domain U defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete\u2013Szeg\u00f6 functional problems and the Taylor\u2013Maclaurin coefficients a2 and a3 for the functions that belong to each of these new subclasses of the bi-univalent function classes. Some more results are revealed after concentrating on the parameters employed in our main results.<\/jats:p>","DOI":"10.3390\/sym15030576","type":"journal-article","created":{"date-parts":[[2023,2,23]],"date-time":"2023-02-23T03:25:56Z","timestamp":1677122756000},"page":"576","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials"],"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5183-2654","authenticated-orcid":false,"given":"Abdullah","family":"Alsoboh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24231, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3203-3539","authenticated-orcid":false,"given":"Omar","family":"Alsalhi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24231, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"ref_1","unstructured":"Legendre, A. 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