{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T18:58:26Z","timestamp":1772132306506,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Research Foundation of Korea (NRF)","award":["NRF-2022R1A2C2004874"],"award-info":[{"award-number":["NRF-2022R1A2C2004874"]}]},{"name":"The National Research Foundation of Korea (NRF)","award":["20214000000280"],"award-info":[{"award-number":["20214000000280"]}]},{"name":"The National Research Foundation of Korea (NRF)","award":["RSP2023R440"],"award-info":[{"award-number":["RSP2023R440"]}]},{"name":"The Korea Institute of Energy Technology Evaluation and Planning (KETEP)","award":["NRF-2022R1A2C2004874"],"award-info":[{"award-number":["NRF-2022R1A2C2004874"]}]},{"name":"The Korea Institute of Energy Technology Evaluation and Planning (KETEP)","award":["20214000000280"],"award-info":[{"award-number":["20214000000280"]}]},{"name":"The Korea Institute of Energy Technology Evaluation and Planning (KETEP)","award":["RSP2023R440"],"award-info":[{"award-number":["RSP2023R440"]}]},{"name":"King Saud University","award":["NRF-2022R1A2C2004874"],"award-info":[{"award-number":["NRF-2022R1A2C2004874"]}]},{"name":"King Saud University","award":["20214000000280"],"award-info":[{"award-number":["20214000000280"]}]},{"name":"King Saud University","award":["RSP2023R440"],"award-info":[{"award-number":["RSP2023R440"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate sharp coefficient functionals, like initial four sharp coefficient bounds, sharp Fekete\u2013Szeg\u00f6 functionals, and, for n=1 and 2, sharp Zalcman functionals are evaluated for class of functions associated with tangent functions. Furthermore, we provide some majorization results for some non-vanishing holomorphic functions, whose ratios are related to various domains in the open unit disk.<\/jats:p>","DOI":"10.3390\/axioms12090868","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T08:01:30Z","timestamp":1694160090000},"page":"868","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Zalcman Functional and Majorization Results for Certain Subfamilies of Holomorphic Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2239-6416","authenticated-orcid":false,"given":"Muhammad Ghafar","family":"Khan","sequence":"first","affiliation":[{"name":"Institute of Numerical Sciences, Kohat University of Sciences and Technology, Kohat 26000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2427-2003","authenticated-orcid":false,"given":"Bilal","family":"Khan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1655-5185","authenticated-orcid":false,"given":"Ferdous M. O.","family":"Tawfiq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4429-9393","authenticated-orcid":false,"given":"Jong-Suk","family":"Ro","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"},{"name":"Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"ref_1","first-page":"940","article-title":"Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln","volume":"138","author":"Bieberbach","year":"1916","journal-title":"Sitzungsberichte Preuss. Akad. 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