Extremal Problems for Functions Starlike in the Exterior of the Unit Circle
1962 ◽
Vol 14
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pp. 540-551
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Keyword(s):
Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.
1965 ◽
Vol 17
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pp. 335-341
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Keyword(s):
1956 ◽
Vol 52
(1)
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pp. 49-60
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Keyword(s):
1932 ◽
Vol 28
(3)
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pp. 266-272
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2015 ◽
Vol 99
(3)
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pp. 315-333
Keyword(s):
2015 ◽
Vol 69
(2)
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pp. 47
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2017 ◽
Vol 25
(3)
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pp. 199-214
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