{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T11:27:47Z","timestamp":1764588467795,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T00:00:00Z","timestamp":1700438400000},"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 the last few years, numerous subfamilies of univalent functions, whether directly or indirectly associated with exponential functions, have been introduced and thoroughly investigated. Among these, the families Se*, Ce and Re defined by subordination to ez have been intensively investigated. While the coefficient problem on the class Se* and Ce has been solved in many cases, in this paper, we mainly intend to compute the sharp estimates of some initial coefficients, the Feketo\u2013Szeg\u00f6 inequality, and the sharp bounds of second- and third-order Hankel determinants for functions belonging to the class Re. This work has the potential to significantly enrich and enhance the exploration of univalent functions in conjunction with exponential functions, making the field more comprehensive and robust.<\/jats:p>","DOI":"10.3390\/sym15112090","type":"journal-article","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T10:32:32Z","timestamp":1700476352000},"page":"2090","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Some Analysis of the Coefficient-Related Problems for Functions of Bounded Turning Associated with a Symmetric Image Domain"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1484-7643","authenticated-orcid":false,"given":"Muhammad","family":"Arif","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9344-2008","authenticated-orcid":false,"given":"Reem K.","family":"Alhefthi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Breaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0269-0688","authenticated-orcid":false,"given":"Lumini\u0163a-Ioana","family":"Cot\u00eerl\u0103","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eleonora","family":"Rapeanu","sequence":"additional","affiliation":[{"name":"Mircea cel Batran Naval Academy, 900218 Constan\u0163a, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,20]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"\u00dcber den Variabilit\u00e4tsbereich der Fourier\u2019schen Konstanten von position harmonischen Funktionen","volume":"32","year":"1911","journal-title":"Comptes Rendus Math."},{"key":"ref_2","first-page":"940","article-title":"\u00dcber di\u00e9 koeffizienten derjenigen Potenzreihen welche eine schlichte Abbildung des Einheitskreises vermitteln","volume":"138","author":"Bieberbach","year":"1916","journal-title":"Sitzungsberichte Preuss. 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