We study locally univalent functions f analytic in the unit disc D of the complex plane such that |f"(z)/f'(z)| (1 − |z|2) ≤ 1 + C(1 − |z|) holds for all z ∈ D, for some C ∈ (0,∞). If C ≤ 1, then f is univalent by Becker's ...