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Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination
(University of Nis, 2018) Srivastava, Hari M.; Sakar, Fethiye Müge; Güney, Hatun Özlem
In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f (z)z, f′ (z) and z f′′ (z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.