Estimations of the second coefficient of a univalent, bounded, symmetric and non-vanishing function by means of Loewner's parametric method
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J. Śladkowska (1998)
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By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions becomes evident in the results obtained.
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Trimble, S.Y. (1987)
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Haakon Waadeland (1980)
Annales Polonici Mathematici
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Abstract. Let S denote the family of functions f, holomorphic and univalent in the open unit disk U, and normalized by f(0) = 0, f'(0) = 1.