{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T02:53:34Z","timestamp":1772765614487,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The normalized analytic function \u03a6N(z)=1+z\u2212z33, which connects the open unit disk onto a bounded domain within the right half of a nephroid-shaped region, is associated with the bounded turning of functions denoted by Rn. It calculates the sharp coefficient inequalities, which include the upper bound of the third Hankel determinant and Logarithmic coefficients related to the functions of the \u03a6N(z) class. This research mainly focuses on identifying solutions to specific coefficient-related problems for analytic functions within the domain of nephroid functions.<\/jats:p>","DOI":"10.3390\/axioms14020136","type":"journal-article","created":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T03:41:47Z","timestamp":1739763707000},"page":"136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Certain Analytic Functions Associated with Nephroid Function"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4246-5849","authenticated-orcid":false,"given":"Wahid","family":"Ullah","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1602-1098","authenticated-orcid":false,"given":"Rabia","family":"Fayyaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0095-1346","authenticated-orcid":false,"given":"Daniel","family":"Breaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s00009-016-0829-y","article-title":"Third Hankel determinants for subclasses of univalent functions","volume":"14","author":"Zaprawa","year":"2017","journal-title":"Mediterr. 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