On the equation \(f(z)=(\beta z+\alpha)f(a)\) in the class of univalent functions
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Goluzin, G. M., Geometričeskaya teoriya funkciĭ kompleksnogo peremennogo. (Russian) [Geometrical theory of functions of a complex variable.] Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1952. 540 pp., MR0056683.
Mocanu, Petru T. On the equation f(z)=αf(a) in the class of univalent functions. Mathematica (Cluj) 6 (29) 1964 63-79, MR0190318.
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