{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T19:59:03Z","timestamp":1780343943259,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T00:00:00Z","timestamp":1669593600000},"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 study, a new class R\u03a3\u03bc(x,\u03b3,\u03b1,\u03b4,\u03b2) of bi-univalent functions studied by means of Gegenbauer polynomials (GP) with Rabotnov functions is introduced. The coefficient of the Taylor coefficients a2 and a3 and Fekete-Szeg\u00f6 problems for functions belonging to R\u03a3\u03bc(x,\u03b3,\u03b1,\u03b4,\u03b2) have been derived as well. Furthermore, a variety of new results will appear by considering the parameters in the main results.<\/jats:p>","DOI":"10.3390\/axioms11120680","type":"journal-article","created":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T02:09:58Z","timestamp":1669687798000},"page":"680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["An Application of Rabotnov Functions on Certain Subclasses of Bi-Univalent Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9287-7704","authenticated-orcid":false,"given":"Ala","family":"Amourah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0745-3347","authenticated-orcid":false,"given":"Ibtisam","family":"Aldawish","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh 11564, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1996-2579","authenticated-orcid":false,"given":"Khadeejah Rasheed","family":"Alhindi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computer Science and Information Technology, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8608-8063","authenticated-orcid":false,"given":"Basem Aref","family":"Frasin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,28]]},"reference":[{"key":"ref_1","first-page":"53","article-title":"Equilibrium of an Elastic Medium with After-Effect","volume":"12","author":"Rabotnov","year":"1948","journal-title":"Prikl. Mat. Mekhanika"},{"key":"ref_2","first-page":"554","article-title":"Sur la nouvelle fonction E(x)","volume":"137","year":"1903","journal-title":"C. R. Acad. Sci. 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