{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T03:07:16Z","timestamp":1781060836754,"version":"3.54.1"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T00:00:00Z","timestamp":1718841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Oradea"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Various researchers have considered different forms of bi-univalent functions in recent times, and this has continued to gain more attention in Geometric Function Theory (GFT), but not much study has been conducted in the area of application of the certain probability concept in geometric functions. In this manuscript, our motivation is the application of analytic and bi-univalent functions. In particular, the researchers examine bi-univalency of a generalized distribution series related to Bell numbers as a family of Caratheodory functions. Some coefficients of the class of the function are obtained. The results are new as far work on bi-univalency is concerned.<\/jats:p>","DOI":"10.3390\/sym16060773","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T05:27:19Z","timestamp":1718861239000},"page":"773","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Quasi-Subordination for Bi-Univalency Involving Generalized Distribution Series"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4651-6876","authenticated-orcid":false,"given":"Sunday Olufemi","family":"Olatunji","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Federal University of Technology, Akure 460114, Ondo State, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3170-6818","authenticated-orcid":false,"given":"Matthew Olanrewaju","family":"Oluwayemi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Margaret Lawrence University, Galilee 321108, Delta State, Nigeria"},{"name":"SDG 4 (Quality Education Research Group), Landmark University, Omu-Aran 251103, Kwara State, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0847-3550","authenticated-orcid":false,"given":"Saurabh","family":"Porwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ram Sahay Government Degree College, Bairi-Shivrajpur, Kanpur 209205, Uttar Pradesh, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7535","authenticated-orcid":false,"given":"Alina","family":"Alb Lupas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, Str. Universitatii nr. 1, 410087 Oradea, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,20]]},"reference":[{"key":"ref_1","first-page":"2214","article-title":"On quasi-subordination for bi-univalency involving generalized distribution series associated with remodelled s-sigmoid function","volume":"14","author":"Olatunji","year":"2023","journal-title":"Int. J. Nonlinear Anal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations. Theory and Applications, Series of Monographs and Text Books in Pure and Applied Mathematics, Marcel Dekker.","DOI":"10.1201\/9781482289817"},{"key":"ref_3","unstructured":"Ma, W.C., and Minda, D. (1994). A Unified Treatment of Some Special Cases of Univalent Functions. Lecture Notes Anal. 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