{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:42:17Z","timestamp":1762522937457,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2024-9\/1"],"award-info":[{"award-number":["QU-APC-2024-9\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present investigation, we introduce a new subclass of univalent functions F(u,\u03bb) and a subclass of bi-univalent function Fo,\u03a3(u,\u03bb) with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes F(u,\u03bb) are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class Fo,\u03a3(u,\u03bb) are established.<\/jats:p>","DOI":"10.3390\/sym16070839","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T08:45:34Z","timestamp":1719996334000},"page":"839","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Ozaki Close-to-Convex Functions with Bounded Boundary Rotation"],"prefix":"10.3390","volume":"16","author":[{"given":"Prathviraj","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asma","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraidah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Srikandan","family":"Sivasubramanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University College of Engineering Tindivanam, Anna University, Tindivanam 604001, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Buraidah 51452, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1307\/mmj\/1028988895","article-title":"Close-to-convex schlicht functions","volume":"1","author":"Kaplan","year":"1952","journal-title":"Mich. 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