doiSerbia

Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Srivastava H.M. (Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada + Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, Republic of China)
Sakar Müge F. (Department of Business Administration, Faculty of Management and Economics, Batman University, Batman, Turkey)
Özlem Güney H. (Department of Mathematics, Faculty of Science, Dicle University, Diyarbakır, Turkey)

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.

Keywords: analytic functions, univalent functions, bi-univalent functions, linear combination, Faber polynomials, Taylor-Maclaurin coefficients, Carathéodory lemma