{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:08Z","timestamp":1740134528909,"version":"3.37.3"},"reference-count":7,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002532","name":"Kyungsung University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002532","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>For real numbers<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><\/mml:math>such that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mn mathvariant=\"normal\">0<\/mml:mn><mml:mo>\u2264<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>&lt;<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo>&lt;<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:math>, we denote by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>\ud835\udca6<\/mml:mi><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:math>the class of normalized analytic functions which satisfy the following two sided-inequality:<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>\u03b1<\/mml:mi><mml:mo>&lt;<\/mml:mo><mml:mi>\u211c<\/mml:mi><mml:mfenced open=\"{\" close=\"}\" separators=\"|\"><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>+<\/mml:mo><mml:mfenced separators=\"|\"><mml:mrow><mml:mrow><mml:mrow><mml:mi>z<\/mml:mi><mml:msup><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">\u2032\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><mml:mo>&lt;<\/mml:mo><mml:mi>\u03b2<\/mml:mi><mml:mo>\u2009<\/mml:mo><mml:mo>\u2009<\/mml:mo><mml:mfenced separators=\"|\"><mml:mrow><mml:mi>z<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>\ud835\udd4c<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>,<\/mml:mo><\/mml:math>where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>\ud835\udd4c<\/mml:mi><\/mml:mrow><\/mml:math>denotes the open unit disk. We find some relationships involving functions in the class<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>\ud835\udca6<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>. And we estimate the bounds of coefficients and solve the Fekete-Szeg\u00f6 problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.<\/jats:p>","DOI":"10.1155\/2013\/294378","type":"journal-article","created":{"date-parts":[[2013,5,27]],"date-time":"2013-05-27T17:00:44Z","timestamp":1369674044000},"page":"1-6","source":"Crossref","is-referenced-by-count":3,"title":["On Certain Classes of Convex Functions"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6741-9752","authenticated-orcid":true,"given":"Young Jae","family":"Sim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 608-736, Republic of Korea"}]},{"given":"Oh Sang","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 608-736, Republic of Korea"}]}],"member":"311","reference":[{"key":"3","first-page":"21","volume":"1772","year":"2011","journal-title":"RIMS Kokyuroku"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.09.012"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2010.05.009"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.11.013"},{"year":"2000","key":"4"},{"key":"5","first-page":"48","volume":"48","year":"1943","journal-title":"Proceedings of the London Mathematical Society"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1969-0232926-9"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/294378.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/294378.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/294378.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T08:12:09Z","timestamp":1469866329000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/294378\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":7,"alternative-id":["294378","294378"],"URL":"https:\/\/doi.org\/10.1155\/2013\/294378","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2013]]}}}