{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T08:21:33Z","timestamp":1762071693442,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T00:00:00Z","timestamp":1666828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571299"],"award-info":[{"award-number":["11571299"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete\u2013Szeg\u00f6-type inequalities for functions in each of these subclasses are obtained. The results derived in this article are shown to extend and generalize those in some earlier works.<\/jats:p>","DOI":"10.3390\/axioms11110595","type":"journal-article","created":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T20:37:58Z","timestamp":1666903078000},"page":"595","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Applications of the q-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials"],"prefix":"10.3390","volume":"11","author":[{"given":"Ying","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Yangzhou University, Yangzhou 225002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7581-615X","authenticated-orcid":false,"given":"Rekha","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"}]},{"given":"Jin-Lin","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yangzhou University, Yangzhou 225002, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,27]]},"reference":[{"key":"ref_1","first-page":"64","article-title":"On q-functions and a certain difference operator","volume":"46","author":"Jackson","year":"1908","journal-title":"Trans. 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