{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:04:10Z","timestamp":1760238250339,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,26]],"date-time":"2020-07-26T00:00:00Z","timestamp":1595721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2017R1C1B5076778"],"award-info":[{"award-number":["2017R1C1B5076778"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let f\u2208A, the class of normalized analytic functions defined in the unit disk D, and be given by f(z)=z+\u2211n=2\u221eanzn for z\u2208D. This paper presents a new approach to finding bounds for |an|. As an application, we find the sharp bound for |a5| for the class B1(\u03b1) of Bazilevi\u010d functions when \u03b1\u22651.<\/jats:p>","DOI":"10.3390\/sym12081228","type":"journal-article","created":{"date-parts":[[2020,7,27]],"date-time":"2020-07-27T09:24:49Z","timestamp":1595841889000},"page":"1228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Fifth Coefficient of Bazilevi\u010d Functions"],"prefix":"10.3390","volume":"12","author":[{"given":"Oh Sang","family":"Kwon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Derek Keith","family":"Thomas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Swansea University, Bay Campus, Swansea SA1 8EN, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6741-9752","authenticated-orcid":false,"given":"Young Jae","family":"Sim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Thomas, D.K., Tuneski, N., and Vasudevarao, A. (2018). Univalent Functions: A Primer, Walter de Gruyter GmbH. De Gruyter Studies in Mathematics 69.","DOI":"10.1515\/9783110560961"},{"key":"ref_2","first-page":"261","article-title":"On Bazilevi\u010d Functions","volume":"38","author":"Singh","year":"1973","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cho, N.E., and Kumar, V. (2019). On a conjecture for Bazilevi\u010d functions. Bull. Malaysian Math. Soc.","DOI":"10.1007\/s40840-019-00857-y"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1007\/s00009-017-0958-y","article-title":"The fifth and sixth coefficients of Bazilevi\u010d Functions B1(\u03b1)","volume":"14","author":"Marjono","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1515\/crll.1917.147.205","article-title":"\u00dcber Potenzreihen, die im Innern des Einheitskreises beschr\u00e4nkt s\u00ednd","volume":"147","author":"Schur","year":"1917","journal-title":"J. Re\u00edne Angew. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1090\/S0002-9939-1957-0083038-0","article-title":"On the coefficients of meromorphic schlicht functions","volume":"8","author":"Nehari","year":"1957","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1017\/S0004972718001429","article-title":"The sharp bounds of some coefficient functionals over the class of functions convex in the direction of the imaginary axis","volume":"100","author":"Cho","year":"2019","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/s00025-019-1107-7","article-title":"Schur parameters and the Carath\u00e9odory class","volume":"74","author":"Li","year":"2019","journal-title":"Results Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rahman, Q.I., and Schmeisser, G. (2002). Analytic theory of polynomials, London Mathematical Society Monographs, The Clarendon Press, Oxford University Press. New Series, 26.","DOI":"10.1093\/oso\/9780198534938.001.0001"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1228\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:51:47Z","timestamp":1760176307000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/8\/1228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,26]]},"references-count":9,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["sym12081228"],"URL":"https:\/\/doi.org\/10.3390\/sym12081228","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,7,26]]}}}