Abstract
In this paper, we introduce and investigate a new subclass of the a-nalytic and bi-univalent functions in the open unit disk in the complex plane. For the functions belonging to this class, we obtain estimates on the first three coefficients in their Taylor-Maclaurin series expansion. Some interesting corollaries and applications of the results obtained here are also discussed.
Highlights
Introduction and PreliminariesLet A denote the class of all complex-valued analytic functions in the open unit disk U = fz 2 C : jzj < 1g in the complex plane of the form X 1 f (z) = z + a2z2 + a3z3 + = z + anzn; z 2 U: (1.1) n=2by S we shall denote the class of all functions in A which are univalent in U
We introduce and investigate a new subclass of the analytic and bi-univalent functions in the open unit disk in the complex plane
For the functions belonging to this class, we obtain estimates on the ...rst three coe¢ cients in their Taylor-Maclaurin series expansion
Summary
These classes denoted, respectively, by S ( ) and C ( ) : An analytic function f 2 S is said to be bi- starlike of Ma-Minda type or biconvex of Ma-Minda type if both f and f 1 are, respectively, Ma-Minda starlike or Ma-Minda convex functions. C ( ) : In the sequel, it is assumed that is an analytic function with positive real part in U , satisfying (0) = 1; 0(0) > 0 and (U ) is starlike with respect to 1 and symmetric with respect to the real axis. Such a function has a series expansion of the following form:. Let denote the class of bi-univalent functions in U given by (1.1)
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