Coefficients and integral means of some classes of analytic functions

Author:
T. Sheil-Small

Journal:
Proc. Amer. Math. Soc. **88** (1983), 275-282

MSC:
Primary 30C45; Secondary 30C50

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695258-8

MathSciNet review:
695258

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Abstract | References | Similar Articles | Additional Information

Abstract: The sharp coefficient bounds for the classes of functions of bounded boundary rotation are obtained by a short and elementary argument. Elementary methods are also applied for the coefficients of related classes characterised by a generalised Kaplan condition. The result is proved simply. It is further shown that the functions are extremal for the th means ( an arbitrary real) of all Kaplan classes .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695258-8

Keywords:
Functions of bounded boundary rotation,
starlike functions,
close-to-convex functions

Article copyright:
© Copyright 1983
American Mathematical Society