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. Ser. A I**523**(1973), 18. MR**0338343****[2]**L. Brickman, D. J. Hallenbeck, T. H. MacGregor, and D. R. Wilken,*Convex hulls and extreme points of families of starlike and convex mappings*, Trans. Amer. Math. Soc.**185**(1973), 413–428 (1974). MR**0338337**, https://doi.org/10.1090/S0002-9947-1973-0338337-5**[3]**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**, https://doi.org/10.1090/S0002-9947-1971-0274734-2**[4]**Peter L. Duren,*Theory of 𝐻^{𝑝} spaces*, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR**0268655****[5]**D. J. Hallenbeck and T. H. MacGregor,*Subordination and extreme-point theory*, Pacific J. Math.**50**(1974), 455–468. MR**0361035****[6]**Hugh M. Hilden,*A characterization of the extreme points of some convex sets of analytic functions*, Duke Math. J.**37**(1970), 715–723. MR**0271737****[7]**Thomas H. MacGregor,*Applications of extreme-point theory to univalent functions*, Michigan Math. J.**19**(1972), 361–376. MR**0311885****[8]**John V. Ryff,*Subordinate 𝐻^{𝑝} functions*, Duke Math. J.**33**(1966), 347–354. MR**0192062**

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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