{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T14:58:57Z","timestamp":1783609137617,"version":"3.55.0"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T00:00:00Z","timestamp":1681084800000},"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>Several different subclasses of the bi-univalent function class \u03a3 were introduced and studied by many authors using distribution series like Pascal distribution, Poisson distribution, Borel distribution, the Mittag-Leffler-type Borel distribution, Miller\u2013Ross-Type Poisson Distribution. In the present paper, by making use of the Bell distribution, we introduce and investigate a new family G\u03a3t(x,p,q,\u03bb,\u03b2,\u03b3) of normalized bi-univalent functions in the open unit disk U, which are associated with the Horadam polynomials and estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to this class. Furthermore, we establish the Fekete\u2013Szeg\u00f6 inequality for functions in the family G\u03a3t(x,p,q,\u03bb,\u03b2,\u03b3). After specializing the parameters used in our main results, a number of new results are demonstrated to follow.<\/jats:p>","DOI":"10.3390\/axioms12040362","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T07:11:43Z","timestamp":1681110703000},"page":"362","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bell Distribution Series Defined on Subclasses of Bi-Univalent Functions That Are Subordinate to Horadam Polynomials"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0745-3347","authenticated-orcid":false,"given":"Ibtisam","family":"Aldawish","sequence":"first","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\/0000-0001-8608-8063","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":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,10]]},"reference":[{"key":"ref_1","unstructured":"Legendre, A. 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