{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T05:42:25Z","timestamp":1773812545422,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T00:00:00Z","timestamp":1691625600000},"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>In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carath\u00e9odory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R\u2118 associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete\u2013Szeg\u00f6-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp.<\/jats:p>","DOI":"10.3390\/axioms12080775","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T10:52:40Z","timestamp":1691664760000},"page":"775","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Sharp Coefficient Bounds for a Subclass of Bounded Turning Functions with a Cardioid Domain"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3079-9944","authenticated-orcid":false,"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, 00186 Rome, Italy"}]},{"given":"Nak Eun","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Pukyong National University, Busan 48513, Republic of Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1484-7643","authenticated-orcid":false,"given":"Muhammad","family":"Arif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali khan University Mardan, Mardan 23200, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"key":"ref_1","unstructured":"Duren, P. 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