{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T20:11:12Z","timestamp":1774296672478,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T00:00:00Z","timestamp":1558915200000},"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>This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order \u03b3 ( \u03b3 \u2208 C \\ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( \u03b4 , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( \u03b4 , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.<\/jats:p>","DOI":"10.3390\/sym11050719","type":"journal-article","created":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T11:19:27Z","timestamp":1558955967000},"page":"719","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator"],"prefix":"10.3390","volume":"11","author":[{"given":"Shahid","family":"Mahmood","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Sarhad University of Science &amp; Information Technology, Ring Road, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nusrat","family":"Raza","sequence":"additional","affiliation":[{"name":"Mathematics Section, Women\u2019s College, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eman S. A.","family":"AbuJarad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9851-4103","authenticated-orcid":false,"given":"Gautam","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, Canada"},{"name":"Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan, Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"H. M.","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8940-0569","authenticated-orcid":false,"given":"Sarfraz Nawaz","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Wah Campus 47040, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0898-1221(04)90025-9","article-title":"Integral inequalities in q-calculus","volume":"47","author":"Gauchman","year":"2004","journal-title":"Comput. Math. 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