On some simple sufficient conditions for univalence
On some simple sufficient conditions for univalence
On some simple sufficient conditions for univalence
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ÊÑÖ 1. For α =0(k = 1) in Corollary 1 we get Theorem 1 from [4].<br />
Corollary 1.1. Let f(z) ∈ A. Then<br />
(i) |f ′′ (z)| 4/5 implies f(z) ∈ S ∗ (1/3);<br />
(ii) |f ′′ (z)| 2/3 implies f(z) ∈ S ∗ (1/2); and<br />
(iii) |f ′′ (z)| 1/2 implies f(z) ∈ S ∗ (2/3).<br />
Corollary 2. If f(z) ∈ A and |f ′′ (z)| 2sin(αÔ/2)/(1 + sin(αÔ/2)) = k, z ∈ U,<br />
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