Abstract
We introduce and investigate a new subclass of the function class Σ of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.
Highlights
By S we denote the class of all functions in A which are univalent in U
A function f ∈ A is said to be biunivalent in U, if f(z) and f−1(z) are univalent in U
Let Σ denote the class of biunivalent functions in U given by (1)
Summary
By S we denote the class of all functions in A which are univalent in U. Let Σ denote the class of biunivalent functions in U given by (1). . .), by using the Gaussian hypergeometric function given by (7), Hohlov [2, 3] introduced the familiar convolution operator Ia,b,c as follows: Ia,b;cf (z) = z 2F1 (a, b, c; z) ∗ f (z) ,
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