{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:56:25Z","timestamp":1760237785931,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T00:00:00Z","timestamp":1592784000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Grant Scheme (FRGS)","award":["FRGS\/1\/2019\/STG06\/UKM\/01\/1"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UKM\/01\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class    A    of normalized analytic functions, where class    A    is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.<\/jats:p>","DOI":"10.3390\/sym12061043","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T07:14:19Z","timestamp":1592982859000},"page":"1043","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers"],"prefix":"10.3390","volume":"12","author":[{"given":"Muhammad","family":"Shafiq","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari 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"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8805-6452","authenticated-orcid":false,"given":"Qazi Zahoor","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9138-916X","authenticated-orcid":false,"given":"Maslina","family":"Darus","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samiha","family":"Kiran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s40995-019-00815-0","article-title":"Operators of basic (or q-) calculus and fractional q-calculus and their applications in Geometric Function Theory of Complex Analysis","volume":"44","author":"Srivastava","year":"2020","journal-title":"Iran. 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