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Coefficient bounds for a certain class of analytic and bi-univalent functions

Srivastava H.M. (University of Victoria, Department of Mathematics and Statistics, Victoria, British Columbia VWR, Canada)
Eker Sevtap Sümer (Dicle University, Faculty of Science, Department of Mathematics, Diyarbakır, Turkey)
Alic Rosihan M. (Universiti Sains Malaysia, School of Mathematical Sciences, USM Penang, Malaysia)

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

Keywords: analytic functions, univalent functions, faber polynomials, bi-univalent functions, Taylor-Maclaurin series expansion, coefficient bounds and coefficient estimates, Taylor-Maclaurin coefficients