{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T21:44:43Z","timestamp":1780609483530,"version":"3.54.1"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T00:00:00Z","timestamp":1703808000000},"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 objective of the present article is to introduce new subclasses of bi-Bazilevi\u010d functions, bi-quasi-convex functions and \u03b1-exponentially bi-convex functions involving functions with bounded boundary rotation of order \u03bd. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete\u2013Szeg\u00f6 coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature.<\/jats:p>","DOI":"10.3390\/axioms13010025","type":"journal-article","created":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T11:19:21Z","timestamp":1703848761000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Initial Coefficient Bounds for Certain New Subclasses of bi-Bazilevi\u010d Functions and Exponentially bi-Convex Functions with Bounded Boundary Rotation"],"prefix":"10.3390","volume":"13","author":[{"given":"Prathviraj","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Srikandan","family":"Sivasubramanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, Tamilnadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nak Eun","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"311","DOI":"10.4064\/ap-31-3-311-323","article-title":"Properties of a class of functions with bounded boundary rotation","volume":"31","author":"Padmanabhan","year":"1976","journal-title":"Ann. 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