{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:34:42Z","timestamp":1776749682157,"version":"3.51.2"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2017R1C1B5076778, 2016R1D1A1A09916450"],"award-info":[{"award-number":["NRF-2017R1C1B5076778, 2016R1D1A1A09916450"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, we find sufficient conditions for starlikeness and convexity of normalized Lommel functions of the first kind using the admissible function methods. Additionally, we investigate some inclusion relationships for various classes associated with the Lommel functions. The functions belonging to these classes are related to the starlike functions, convex functions, close-to-convex functions and quasi-convex functions.<\/jats:p>","DOI":"10.3390\/sym10100455","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Geometric Properties of Lommel Functions of the First Kind"],"prefix":"10.3390","volume":"10","author":[{"given":"Young Jae","family":"Sim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oh Sang","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kyungsung University, Busan 48434, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nak Eun","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/BF01443342","article-title":"Ueber eine mit den Besselschen Functionen verwandte Function","volume":"9","author":"Lommel","year":"1876","journal-title":"Math. 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Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s40840-015-0180-7","article-title":"Close-to-convexity of some special functions and their derivatives","volume":"39","author":"Baricz","year":"2016","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1090\/S0002-9947-1969-0232920-2","article-title":"Convex and starlike univalent functions","volume":"35","author":"Bernardi","year":"1969","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1137\/0515057","article-title":"Starlike and prestarlike hypergeometric functions","volume":"159","author":"Carlson","year":"1984","journal-title":"SIAM J. Math. 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