A generalization of univalent functions with bounded boundary rotation
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- by Edward J. Moulis PDF
- Trans. Amer. Math. Soc. 174 (1972), 369-381 Request permission
Abstract:
This paper introduces a class of functions which generalizes both those functions $f(z)$ with bounded boundary rotation and those functions for which $zf’(z)$ is a-spirallike. A simple variational formula for this class is derived and used to determine sufficient conditions for the univalency of functions there in. Various representations for these functions are given, and these are used to derive another condition for univalence; this one is the best known so far in the subclass consisting of functions $f(z)$ for which $zf’(z)$ is a-spirallike. Bounds on the modulus of the Schwarzian derivative are also derived; these are sharp in the subclass of functions having bounded boundary rotation.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 174 (1972), 369-381
- MSC: Primary 30A32
- DOI: https://doi.org/10.1090/S0002-9947-1972-0320296-1
- MathSciNet review: 0320296