On the extreme points of some sets of analytic functions

Author:
John G. Milcetich

Journal:
Proc. Amer. Math. Soc. **45** (1974), 223-228

MSC:
Primary 30A76

DOI:
https://doi.org/10.1090/S0002-9939-1974-0352470-X

MathSciNet review:
0352470

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the set of analytic functions defined on the open unit disc. The extreme points of and are determined. Also a partial characterization is given for the extreme points of and .

**[1]**D. A. Brannan, J. G. Clunie and W. E. Kirwan,*On the coefficient problem for functions of bounded boundary rotation*, Ann. Acad. Sci. Fenn. AI, no. 523 (1973), 18 pp. MR**0338343 (49:3108)****[2]**L. Brickman, D. J. Hallenbeck, T. H. Mac Gregor and D. R. Wilken,*Convex hulls and extreme points of families of starlike and convex mappings*, Trans. Amer. Math. Soc.**185**(1973), 413-428. MR**0338337 (49:3102)****[3]**L. Brickman, T. H. Mac Gregor and D. R. Wilken,*Convex hulls of some classical families of univalent functions*, Trans. Amer. Math. Soc.**156**(1971), 91-107. MR**43**#494. MR**0274734 (43:494)****[4]**P. L. Duren,*Theory of spaces*, Pure and Appl. Math., vol. 38, Academic Press, New York, 1970. MR**42**#3552. MR**0268655 (42:3552)****[5]**D. J. Hallenbeck and T. H. Mac Gregor,*Subordination and extreme point theory*(to appear). MR**0361035 (50:13481)****[6]**H. M. Hilden,*A characterization of the extreme points of some convex sets of analytic functions*, Duke Math. J.**37**(1970), 715-723. MR**42**#6618. MR**0271737 (42:6618)****[7]**T. H. Mac Gregor,*Applications of extreme point theory to univalent functions*, Michigan Math. J.**19**(1972), 361-376. MR**0311885 (47:447)****[8]**J. V. Ryff,*Subordinate functions*, Duke Math. J.**33**(1966), 347-354. MR**33**#289. MR**0192062 (33:289)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0352470-X

Keywords:
Extreme points,
subordination,
spaces

Article copyright:
© Copyright 1974
American Mathematical Society