Abstract
In this paper, two bounded bi-univalent function subclasses were defined by using Salagean q-differential operator. The functions are defined in the open unit disc of complex plane. The main purpose is to determine some estimations on the initial Maclaurin coefficients for functions in these subclasses. Finally, the Fekete-Szegö inequalities for these are also obtained.
Highlights
Let A denotes the class of analytic functions of the form ∞f (z) = z + akzk, (1)k=2 normalized by the conditions f (0) = f (0) − 1 = 0, which are defined on the open unit disc U = {z ∈ C : |z| < 1}
K=2 normalized by the conditions f (0) = f (0) − 1 = 0, which are defined on the open unit disc U = {z ∈ C : |z| < 1}
In the geometric function theory, there are two important subclasses of S, which are the well-known subclasses of starlike and convex functions, namely, S∗ and K, for which the inequalities Re zf (z)/f (z) > 0 and
Summary
Let S be the subclass of A consisting of all functions of the form (1) which are univalent in U. Let denotes the subclass of S, consisting of all bi-univalent functions defined on the unit disc U. Several authors have introduced and investigated subclasses of bi-univalent functions and obtained bounds for the initial coefficients
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