{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:48:31Z","timestamp":1762177711604,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T00:00:00Z","timestamp":1736467200000},"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>The Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as Sscc(\u03d1,\u039e(x)), which we present and examine in this work. These functions are defined with respect to symmetric conjugate points. Coefficient estimates are obtained for functions in this family. The classical Fekete\u2013Szeg\u00f6 inequality of functions in this family is also obtained.<\/jats:p>","DOI":"10.3390\/axioms14010050","type":"journal-article","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T06:25:54Z","timestamp":1736490354000},"page":"50","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Applications of Lucas Balancing Polynomial to Subclasses of Bi-Starlike Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8285-6619","authenticated-orcid":false,"given":"Gangadharan","family":"Murugusundaramoorthy","sequence":"first","affiliation":[{"name":"School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, India"}]},{"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, 400114 Cluj-Napoca, Romania"}]},{"given":"Daniel","family":"Breaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,10]]},"reference":[{"key":"ref_1","unstructured":"Duren, P. 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