• James A. Jenkins
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 18)


The study of univalent functions to-day consists of the investigation of certain families of functions regular or meromorphic and univalent in prescribed domains which may be simply-or multiplyconnected especially from the aspects of the values which they assume and extremal problems for their coefficients in power series expansions, function values and derivatives. These problems are often closely connected with questions in conformal mapping and indeed in many cases have arisen from them. For the sake of definiteness we give first Definition 1.1. Let the function ƒ (z) be regular or meromorphic in the domain D on the z-sphere. Then ƒ (z) is called univalent if for z1, z2D, z1 = z2, we have
$$ f({z_1}) \ne f({z_2}). $$


RIEMANN Surface Univalent Function Conformal Mapping Extremal Problem Quasiconformal Mapping 
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© Springer-Verlag oHG. Berlin · Göttingen · Heidelberg 1958

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  • James A. Jenkins

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