New support points of and extreme points of

Author:
Kent Pearce

Journal:
Proc. Amer. Math. Soc. **81** (1981), 425-428

MSC:
Primary 30C45

MathSciNet review:
597655

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the usual class of univalent analytic functions on normalized by . We prove that the functions

**[1]**Louis Brickman,*Extreme points of the set of univalent functions*, Bull. Amer. Math. Soc.**76**(1970), 372–374. MR**0255788**, 10.1090/S0002-9904-1970-12483-1**[2]**L. Brickman, T. H. MacGregor, and D. R. Wilken,*Convex hulls of some classical families of univalent functions*, Trans. Amer. Math. Soc.**156**(1971), 91–107. MR**0274734**, 10.1090/S0002-9947-1971-0274734-2**[3]**Louis Brickman and Donald Wilken,*Support points of the set of univalent functions*, Proc. Amer. Math. Soc.**42**(1974), 523–528. MR**0328057**, 10.1090/S0002-9939-1974-0328057-1**[4]**J. E. Brown,*Geometric properties of a class of support points of univalent functions*(manuscript).**[5]**Nelson Dunford and Jacob T. Schwartz,*Linear operators. Part I*, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR**1009162****[6]**G. M. Goluzin,*Geometric theory of functions of a complex variable*, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR**0247039****[7]**E. Grassmann, W. Hengartner, and G. Schober,*Support points of the class of close-to-convex functions*, Canad. Math. Bull.**19**(1976), no. 2, 177–179. MR**0486471****[8]**R. Hornblower and D. R. Wilken,*On the support points of close-to-convex functions*(manuscript).**[9]**W. E. Kirwan and R. W. Pell,*Extremal properties for a class of slit conformal mappings*(manuscript).**[10]**Albert Pfluger,*Lineare Extremalprobleme bei schlichten Funktionen*, Ann. Acad. Sci. Fenn. Ser. A I**489**(1971), 32 (German). MR**0296276**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0597655-6

Keywords:
Support points,
extreme points,
univalent functions,
close-to-convex functions

Article copyright:
© Copyright 1981
American Mathematical Society