Abstract
The main purpose of this paper is to derive some sufficient conditions for analytic functions to be of non-Bazilevič type.
Highlights
Let A denote the class of functions of the form ∞f (z) = z + ∑ajzj, (1)j=2 which are analytic in the open unit disk:U := {z : z ∈ C, |z| < 1} . (2)For 0 ≦ α < 1 and 0 < μ < 1, a function f ∈ A is said to be in the class N(μ, α) if it satisfies the condition R (f (z) (
For 0 ≦ α < 1 and 0 < μ < 1, a function f ∈ A is said to be in the class N(μ, α) if it satisfies the condition α, (z ∈ U)
If there exists a Schwarz function ω, which is analytic in U with ω (0) = 0, |ω (z)| < 1, (z ∈ U), (5)
Summary
J=2 which are analytic in the open unit disk:. U := {z : z ∈ C, |z| < 1}. The class N(μ, α) is said to be non-Bazilevicfunctions of order α (see [1]). If there exists a Schwarz function ω, which is analytic in U with ω (0) = 0, |ω (z)| < 1, (z ∈ U) , Such that f (z) = g (ω (z)) , (z ∈ U). If the function g is univalent in U, we have the following equivalence:. Let φ be analytic in the domain D containing q(U) with φ(ω) ≠ 0 when ω ∈ q(U).
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