An Extension of the Region of Variability of a Subclass of Univalent Functions
نویسندگان
چکیده
We show that for α ∈ (0, 2], if f ∈ A with f ′(z) 6= 0, z ∈ E, satisfies the condition (1− α)f ′(z) + α ( 1 + zf ′′(z) f ′(z) ) ≺ F (z), then f is univalent in E, where F is the conformal mapping of the unit disk E with F (0) = 1 and F (E) = C \ { w ∈ C : < w = α, |= w| ≥ √ α(2− α) } . Our result extends the region of variability of the differential operator (1− α)f ′(z) + α ( 1 + zf ′′(z) f ′(z) ) , implying univalence of f ∈ A in E, for 0 < α ≤ 2.
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