Criteria for the extremality of the Koebe mapping
Authors:
D. Bshouty and W. Hengartner
Journal:
Proc. Amer. Math. Soc. 111 (1991), 403411
MSC:
Primary 30C50; Secondary 30C55
MathSciNet review:
1037204
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Abstract: A criterion is developed which gives a necessary condition on a real functional in order that the Koebe Mapping be extremal for this functional in the well known class of normalized univalent functions. This is applied to the coefficient problem of as well as to the problem of univalence of sections of the power series expansion of .
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 [1]
 D. Bshouty and W. Hengartner, Local behaviour of coefficients in subclasses of S, Contemp. Math. Amer. Math. Soc. 38 (1985), 7784. MR 789448
 [2]
 , A variation of the Koebe mapping in a dense subset of S, Canad. J. Math. 39 (1987), 5473. MR 889106 (88j:30048)
 [3]
 P. L. Duren, Univalent functions, SpringerVerlag, New York and Berlin, 1983. MR 708494 (85j:30034)
 [4]
 A. Z. Grinshpan, On the power stability for the Bieberbach inequality, Analytic Number Theory and the Theory of Functions, 5, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 125 (1983), 5864. MR 697766 (85a:30030)
 [5]
 A. Z. Grinshpan and I. M. Milin, Logarithmic coefficients means of univalent functions, Complex Variables Theory Appl. 7 (1986), 139147. MR 877659 (88d:30022)
 [6]
 W. K. Hayman and J. A. Hummel, Coefficients of powers of univalent functions, Complex Variables Theory Appl. 7 (1986), 5170. MR 877651 (88d:30020)
 [7]
 M. S. Robertson, The partial sums of multivalently starlike functions, Ann. of Math. 42 (1941), 829838. MR 0004905 (3:79b)
 [8]
 C. Schaeffer and D. C. Spencer, Coefficients of Schlicht functions, Duke Math. J. 10 (1943), 611635. MR 0009631 (5:175i)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199110372048
PII:
S 00029939(1991)10372048
Article copyright:
© Copyright 1991 American Mathematical Society
