The theory of sharp first-order univalence criteria |
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Authors: | Julian Gevirtz |
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Institution: | 1. Facultad de Matemáticas, Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
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Abstract: | A condition of the formf′ (D) ⊂R is calleda first-order univalence criterion if all functions for which it holds are univalent inD. By means of a careful analysis of the behavior of the corresponding extremal functions, we establish fundamental principles
for a coherent theory of sharp criteria of this kind. In particular, we examine the relationship between three different concepts
of sharpness and show how large classes of first-order univalence criteria which are sharp in a strong sense may be described
in terms of the univalence properties of families of analytic functions depending on a finite number of parameters.
This research was supported in part by the Chilean government through FONDECYT grant No. 0809-91. |
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