{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:02:02Z","timestamp":1760058122144,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T00:00:00Z","timestamp":1741910400000},"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 study, we introduce and explore the properties of the m-leaf function Qm defined in the open unit disk D, where m\u2208N, and this function is defined by the relation Qm(z):=1+m+1m+2z+1m+2zm+1. We determine the main geometrical characterization of this function, focusing on its univalency and its sharp bounds for the real and imaginary modulus. Also, we find radius of convexity, and we give a subordination and inclusion result. Using this function, we introduce a new subclass of analytic functions normalized as usual in D denoted by Amr,s, and an investigation of this class reveals some interesting properties.<\/jats:p>","DOI":"10.3390\/sym17030438","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T13:07:51Z","timestamp":1741957671000},"page":"438","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Geometric Properties of the m-Leaf Function and Connected Subclasses"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8980-9671","authenticated-orcid":false,"given":"Baskaran","family":"Sudharsanan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Agurchand Manmull Jain College, Meenambakkam, Chennai 600061, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5706-4174","authenticated-orcid":false,"given":"Saravanan","family":"Gunasekar","sequence":"additional","affiliation":[{"name":"PG and Research Department of Mathematics, Pachaiyappa\u2019s College, Chennai 600030, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8026-218X","authenticated-orcid":false,"given":"Teodor","family":"Bulboac\u0103","sequence":"additional","affiliation":[{"name":"Research Center of Applied Analysis, Faculty of Mathematics and Computer Science, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"ref_1","unstructured":"Deo, N., Gupta, V., Acu, A., and Agrawal, P. (2020). Radius estimates for three leaf function and convex combination of starlike functions. Mathematical Analysis I: Approximation Theory. ICRAPAM 2018, Springer."},{"key":"ref_2","first-page":"8356125","article-title":"Some sharp results on coefficient estimate problems for four-feaf-type bounded turning functions","volume":"2022","author":"Sunthrayuth","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref_3","first-page":"2621811","article-title":"The second Hankel determinant of logarithmic coefficients for starlike and convex functions involving four-leaf-shaped domain","volume":"2022","author":"Alshehry","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref_4","first-page":"48","article-title":"\u00dcber die konforme Abbildund Sterngebieten","volume":"63","author":"Nevanlinna","year":"1921","journal-title":"Oversikt Fin. Soc. Forh."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Goluzin, G.M. (1969). 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Lectures on the Theory of Functions, Oxford University Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0305004100020703","article-title":"On subordinate functions","volume":"35","author":"Rogosinski","year":"1939","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_11","first-page":"48","article-title":"On the coefficients of subordinate functions","volume":"48","author":"Rogosinski","year":"1943","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Gunasekar, S., Sudharsanan, B., Ibrahim, M., and Bulboac\u0103, T. (2024). Subclasses of analytic functions subordinated to the four-leaf function. Axioms, 13.","DOI":"10.3390\/axioms13030155"},{"key":"ref_13","unstructured":"Duren, P.L. (1983). Univalent Functions. Grundlehren der Mathemalischen Wissenstfhaften, Springer."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/438\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:53:56Z","timestamp":1760028836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/438"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,14]]},"references-count":13,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030438"],"URL":"https:\/\/doi.org\/10.3390\/sym17030438","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,14]]}}}