{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:55Z","timestamp":1760148655429,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T00:00:00Z","timestamp":1685491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]},{"name":"Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]},{"name":"Natural Science Foundation of Inner Mongolia of China","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]},{"name":"Higher School Foundation of Inner Mongolia of China","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]},{"name":"Natural Science Foundation of Anhui Provincial Department of Education","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]},{"name":"program of Guangzhou Civil Aviation college","award":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"],"award-info":[{"award-number":["11561001","11271045","NJYT-18-A14","2018MS01026","2020MS01010","NJZY19211","KJ2020A0993","KJ2020ZD74","22x0418"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>LetN be the class of functions that convex in one direction and M denote the class of functions zf\u2032(z), where f\u2208N. In the paper, the third-order Hankel determinants for these classes are estimated. The estimates of H3,1(f) obtained in the paper are improved.<\/jats:p>","DOI":"10.3390\/sym15061176","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T02:57:10Z","timestamp":1685501830000},"page":"1176","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved Upper Bounds of the Third-Order Hankel Determinant for Ozaki Close-to-Convex Functions"],"prefix":"10.3390","volume":"15","author":[{"given":"Dong","family":"Guo","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Yangzhou Polytechnic College, Yangzhou 225009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huo","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Students\u2019 Affairs Office, Chuzhou Polytechnic College, Chuzhou 239000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongtao","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Humanities and Social Sciences, Guangzhou Civil Aviation College, Guangzhou 510403, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingbing","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Basic Disciplines, Chuzhou Polytechnic College, Chuzhou 239000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4153-5605","authenticated-orcid":false,"given":"En","family":"Ao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Chifeng University, Chifeng 024000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,31]]},"reference":[{"key":"ref_1","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":"41","author":"Pommerenke","year":"1966","journal-title":"J. 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