Cheng, YingSrivastava, RekhaLiu, Jin-Lin2022-11-132022-11-1320222022Cheng, Y., Srivastava, R., & Liu, J. (2022). “Applications of the q-derivative operator to new families of bi-univalent functions related to the Legendre polynomials.” Axioms, 11(11), 595. https://doi.org/10.3390/axioms11110595https://doi.org/10.3390/axioms11110595http://hdl.handle.net/1828/14459By 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–Szegö-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.enanalytic functionsbi-univalent functionsq-derivative operatorsubordination between analytic functionsLegendre polynomialsFekete–Szegö inequalityArticleDepartment of Mathematics and Statistics