{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:36:42Z","timestamp":1759797402180,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The 2023 Jiangsu Provincial Science and Technology Deputy Director Program","award":["FZ20231182","FZ20231166"],"award-info":[{"award-number":["FZ20231182","FZ20231166"]}]},{"name":"General Program of Natural Science Research (Self-funded) for Higher Education Institutions","award":["ZM202403344"],"award-info":[{"award-number":["ZM202403344"]}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let RLP denote a newly introduced subclass of bounded turning functions. The primary aim of this study is to investigate the sharp bounds of the coefficients of |d2|,|d3|,|d4|,|d5|, as well as to establish precise estimates for the second- and third-order Hankel determinants H2,1,H2,2,H2,3, and H3,1 for functions belonging to this class. The coefficient bounds and Hankel determinant estimates derived herein are all shown to be sharp.<\/jats:p>","DOI":"10.3390\/sym17101668","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T11:42:49Z","timestamp":1759750969000},"page":"1668","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Sharp Coefficients and Hankel Determinants for a Novel Class RLP"],"prefix":"10.3390","volume":"17","author":[{"given":"Chuanjun","family":"Wen","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou Polytechnic University, Yangzhou 225009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou Polytechnic University, Yangzhou 225009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongcan","family":"Diao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou Polytechnic University, Yangzhou 225009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinchao","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Basic Disciplines, Chuzhou Polytechnic College, Chuzhou 239000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21993","DOI":"10.3934\/math.20231121","article-title":"Hankel inequalities for bounded turning functions in the domain of cosine Hyperbolic function","volume":"8","author":"Khan","year":"2023","journal-title":"AIMS Math."},{"key":"ref_2","first-page":"860","article-title":"Sharp Bounds On Hankel Determinants for Certain Subclass of Starlike Functions","volume":"13","author":"Wang","year":"2022","journal-title":"J. Appl. Anal. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1112\/jlms\/s1-41.1.111","article-title":"On the coefficients and Hankel determinants of univalent functions","volume":"1","author":"Pommerenke","year":"1966","journal-title":"J. Lond. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1112\/S002557930000807X","article-title":"On the Hankel determinants of univalent functions","volume":"14","author":"Pommerenke","year":"1967","journal-title":"Mathematika"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"R\u0103ducanu, D. (2022). On Coefficient Estimates for a Certain Class of Analytic Functions. Mathematics, 11.","DOI":"10.3390\/math11010012"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.3906\/mat-1706-83","article-title":"Second Hankel determinant for certain subclasses of bi-univalent functions involving Chebyshev polynomials","volume":"42","author":"Orhan","year":"2018","journal-title":"Turk. J. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Tang, H., Arif, M., Abbas, M., Tawfiq, F.M., and Malik, S.N. (2023). Analysis of Coefficient-Related Problems for Starlike Functions with Symmetric Points Connected with a Three-Leaf-Shaped Domain. Symmetry, 15.","DOI":"10.3390\/sym15101837"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1017\/S0004972717001125","article-title":"The sharp bound for the Hankel determinant of the third kind for convex functions","volume":"97","author":"Kowalczyk","year":"2018","journal-title":"Aust. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wen, C., Li, Z., and Guo, D. (2024). Some Results on Coefficient Estimate Problems for Four-Leaf-Type Bounded Turning Functions. Mathematics, 12.","DOI":"10.20944\/preprints202404.1583.v1"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, D., Ahmad, A., Ikhlas, H., Hussain, S., Noor, S., and Tang, H. (2025). On Sharp Coefficients and Hankel Determinants for a Novel Class of Analytic Functions. Axioms, 14.","DOI":"10.3390\/axioms14030191"},{"key":"ref_11","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_12","first-page":"251","article-title":"Coefficient bounds for the inverse of a function with derivative in P","volume":"87","author":"Libera","year":"1983","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.crma.2015.03.003","article-title":"Bound for the fifth coefficient of certain starlike functions","volume":"353","author":"Ravichandran","year":"2015","journal-title":"Comptes Rendus Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1090\/S0002-9939-1982-0652447-5","article-title":"Early coefficients of the inverse of a regular convex function","volume":"85","author":"Rlibera","year":"1982","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s40315-017-0229-8","article-title":"On the fourth coefficient of functions in the Carath\u00e9odory class","volume":"18","author":"Kwon","year":"2018","journal-title":"Comput. Methods Funct. Theory"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1668\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T11:54:23Z","timestamp":1759751663000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1668"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,6]]},"references-count":15,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["sym17101668"],"URL":"https:\/\/doi.org\/10.3390\/sym17101668","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,6]]}}}