{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:54:59Z","timestamp":1760057699626,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider analytic functions with the formalization f(0)=f\u2032(0)\u22121=0, which satisfy Re{(1\u2212\u03b1z2)f\u2032(z)}&gt;0,z\u2208\u0394={z\u2208C:|z|&lt;1}, where \u03b1\u2208[\u22121,1]. The set of such functions is a subclass of the class of close-to-convex functions. In this paper, we present sharp bounds of |an|, where an is the n\u2212th Taylor\u2019s coefficients for functions in this class. In addition, we consider several symmetric coefficient problems when the second coefficient a2 is established. In particular, we provide bounds of |an+1\u2212an| and of |2na2n\u2212(2n\u22121)a2n\u22121| for the considered class under this additional assumption.<\/jats:p>","DOI":"10.3390\/sym17020310","type":"journal-article","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T05:34:26Z","timestamp":1739943266000},"page":"310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coefficient Estimates in a Class of Close-to-Convex Functions"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9210-3757","authenticated-orcid":false,"given":"Lucyna","family":"Trojnar-Spelina","sequence":"first","affiliation":[{"name":"The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,19]]},"reference":[{"key":"ref_1","first-page":"137","article-title":"A proof of the Bieberbach conjecture, LOMI Preprints, E-5-84, Leningrad 1984","volume":"154","year":"1985","journal-title":"Acta Math."},{"key":"ref_2","unstructured":"Duren, P.L. (1983). Univalent Functions, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1112\/jlms\/s1-38.1.228","article-title":"On successive coefficients of univalent functions","volume":"38","author":"Hayman","year":"1963","journal-title":"Lond. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1112\/blms\/10.2.193","article-title":"Successive coefficients of starlike functions","volume":"10","author":"Leung","year":"1978","journal-title":"Bull Lond. Math. 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