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Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator

Srivastava H.M. (Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia VW R, Canada + Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, Republic of China)
Altınkaya Şahsene (Department of Mathematics, Faculty of Arts and Science, Uludag University, Bursa, Turkey)
Yalçın Sibel (Department of Mathematics, Faculty of Arts and Science, Uludag University, Bursa, Turkey)

In this paper, we discuss the various properties of a newly-constructed subclass of the class of normalized bi-univalent functions in the open unit disk, which is defined here by using a symmetric basic (or q-) derivative operator. Moreover, for functions belonging to this new basic (or q-) class of normalized biunivalent functions, we investigate the estimates and inequalities involving the second Hankel determinant.

Keywords: analytic functions, univalent functions, bi-univalent functions, Hankel determinant, Fekete-Szegö functional, q-Derivative