{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:34:32Z","timestamp":1753882472416,"version":"3.41.2"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,9]],"date-time":"2006-11-09T00:00:00Z","timestamp":1163030400000},"content-version":"vor","delay-in-days":312,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Ministry of Education and Science of the Republic of Macedonia","award":["17\/1383\/1","TBGA-U-105T056"],"award-info":[{"award-number":["17\/1383\/1","TBGA-U-105T056"]}]},{"name":"Scientific and Technical Research Council of Turkey","award":["17\/1383\/1","TBGA-U-105T056"],"award-info":[{"award-number":["17\/1383\/1","TBGA-U-105T056"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Let  be the class of analytic functions in the unit disk that\nare normalized with <jats:italic>f<\/jats:italic>(0) = <jats:italic>f\u2032<\/jats:italic>(0) \u2212 1 = 0 and let \u22121 \u2264 <jats:italic>B<\/jats:italic> &lt; <jats:italic>A<\/jats:italic> \u2264 1. In this paper we study the class <jats:italic>G<\/jats:italic><jats:sub><jats:italic>\u03bb<\/jats:italic>,<jats:italic>\u03b1<\/jats:italic><\/jats:sub> = {<jats:italic>f<\/jats:italic> \u2208 :|(1 \u2212 <jats:italic>\u03b1<\/jats:italic> + <jats:italic>\u03b1<\/jats:italic><jats:italic>z<\/jats:italic><jats:italic>f<\/jats:italic><jats:sup>\u2033<\/jats:sup>(<jats:italic>z<\/jats:italic>)\/<jats:italic>f\u2032<\/jats:italic>(<jats:italic>z<\/jats:italic>))\/<jats:italic>z<\/jats:italic><jats:italic>f\u2032<\/jats:italic>(<jats:italic>z<\/jats:italic>)\/<jats:italic>f<\/jats:italic>(<jats:italic>z<\/jats:italic>)\u2212(1 \u2212 <jats:italic>\u03b1<\/jats:italic>)| &lt; <jats:italic>\u03bb<\/jats:italic>, <jats:italic>z<\/jats:italic>\u2208}, 0 \u2264 <jats:italic>\u03b1<\/jats:italic> \u2264 1,  and give sharp  sufficient conditions that embed it into the classes\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<jats:italic>S<\/jats:italic><jats:sup>\u2217<\/jats:sup>[<jats:italic>A<\/jats:italic>, <jats:italic>B<\/jats:italic>] = {<jats:italic>f<\/jats:italic> \u2208 :<jats:italic>z<\/jats:italic><jats:italic>f\u2032<\/jats:italic>(<jats:italic>z<\/jats:italic>)\/<jats:italic>f<\/jats:italic>(<jats:italic>z<\/jats:italic>)\u227a(1 + <jats:italic>A<\/jats:italic><jats:italic>z)<\/jats:italic>\/(1 + <jats:italic>B<\/jats:italic><jats:italic>z)<\/jats:italic>}\nand <jats:italic>K<\/jats:italic>(<jats:italic>\u03b4<\/jats:italic>) = {<jats:italic>f<\/jats:italic> \u2208 :1 + <jats:italic>z<\/jats:italic><jats:italic>f<\/jats:italic><jats:sup>\u2033<\/jats:sup>(<jats:italic>z<\/jats:italic>)\/<jats:italic>f\u2032<\/jats:italic>(<jats:italic>z<\/jats:italic>)\u227a(1 \u2212 <jats:italic>\u03b4<\/jats:italic>)(1 + <jats:italic>z<\/jats:italic>)\/(1 \u2212 <jats:italic>z<\/jats:italic>) + <jats:italic>\u03b4<\/jats:italic>}, where \u201c\u227a\u201d denotes the usual subordination. Also, sharp upper\nbound of |<jats:italic>a<\/jats:italic><jats:sub>2<\/jats:sub>| and of the Fekete\u2010Szeg\u00f6 functional  is given for the class <jats:italic>G<\/jats:italic><jats:sub><jats:italic>\u03bb<\/jats:italic>,<jats:italic>\u03b1<\/jats:italic><\/jats:sub>.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/38089","type":"journal-article","created":{"date-parts":[[2006,11,16]],"date-time":"2006-11-16T07:16:04Z","timestamp":1163661364000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Starlikeness and convexity of a class of analytic functions"],"prefix":"10.1155","volume":"2006","author":[{"given":"Nikola","family":"Tuneski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00fcseyin","family":"Irmak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,9]]},"reference":[{"key":"e_1_2_1_1_2","first-page":"11","article-title":"New criteria for starlikeness and strongly starlikeness","volume":"43","author":"Bulboac\u0103 T.","year":"2001","journal-title":"Mathematica (Cluj)"},{"key":"e_1_2_1_2_2","series-title":"Fundamental Principles of Mathematical Sciences","volume-title":"Univalent Functions","author":"Duren P. 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