Abstract
In this work, the conditions for univalence, starlikeness and convexity are discussed. MSC:30C45, 30C80.
Highlights
The function q is analytic in |z| ≤ |z | < and from the hypothesis of Theorem
We shall consider the set H of all analytic functions in the open unit disc D = z : |z| α,z ∈ D f (z)
1 Introduction We shall consider the set H of all analytic functions in the open unit disc
Summary
The function q is analytic in |z| ≤ |z | < and from the hypothesis of Theorem . From FukuiSakaguchi [ ] and Jack’s [ ] lemmas, there exists a real number k ≥ such that z q (z ) = z p (z ) – z p (z ) q(z ) p(z ) – p(z ) Proof If there exists a point z , |z | < , such that Re p(z) > α for |z| < |z |
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