{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T02:28:53Z","timestamp":1783650533324,"version":"3.55.0"},"reference-count":56,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T00:00:00Z","timestamp":1697500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research article introduces a novel operator termed q-convolution, strategically integrated with foundational principles of q-calculus. Leveraging this innovative operator alongside q-Bernoulli polynomials, a distinctive class of functions emerges, characterized by both analyticity and bi-univalence. The determination of initial coefficients within the Taylor-Maclaurin series for this function class is accomplished, showcasing precise bounds. Additionally, explicit computation of the second Hankel determinant is provided. These pivotal findings, accompanied by their corollaries and implications, not only enrich but also extend previously published results.<\/jats:p>","DOI":"10.3390\/sym15101928","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T10:43:10Z","timestamp":1697539390000},"page":"1928","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Exploring a Special Class of Bi-Univalent Functions: q-Bernoulli Polynomial, q-Convolution, and q-Exponential Perspective"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5881-9260","authenticated-orcid":false,"given":"Timilehin Gideon","family":"Shaba","sequence":"first","affiliation":[{"name":"Department of Mathematics, Landmark University, P.M.B., Omu-Aran 1001, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3950-6864","authenticated-orcid":false,"given":"Serkan","family":"Araci","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, TR-27010 Gaziantep, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Babatunde Olufemi","family":"Adebesin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Landmark University, P.M.B., Omu-Aran 1001, Nigeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3137-3865","authenticated-orcid":false,"given":"Ayhan","family":"Esi","sequence":"additional","affiliation":[{"name":"Department of Basic Engineering Sciences, Engineering Faculty, Malatya Turgut Ozal University, TR-44040 Malatya, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.cnsns.2010.05.027","article-title":"Recent history of fractional calculus","volume":"16","author":"Machado","year":"2011","journal-title":"Commun. 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