Abstract
In the current paper, by making use of the Horadam polynomials, we introduce and investigate a new family of holomorphic and biunivalent functions with respect to symmetric conjugate points defined in the open unit disk D. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this family.
Highlights
Denote by A the collection of holomorphic functions in the open unit disk D = {z ∈ C : |z| < 1} that have the form: (1.1)X ∞ f (z) = z + anzn. n=2Further, let S indicate the sub-collection of A consisting of functions inD satisfying (1.1) which are univalent in D.let Ss∗c be the subclass of S consisting of functions given by (1.1) satisfying ( ) zf 0(z) Re
Let S indicate the sub-collection of A consisting of functions in
We begin this section by defining the family GΣ(λ, η, r) as follows: Definition 2.1
Summary
Let S indicate the sub-collection of A consisting of functions in Let Ss∗c be the subclass of S consisting of functions given by (1.1) The class can be extended to other class in D, namely convex functions with respect to symmetric conjugate points. Let Csc denote the class of convex functions with respect to symmetric conjugate points and satisfy the conditions
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