Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Criteria for the extremality of the Koebe mapping


Authors: D. Bshouty and W. Hengartner
Journal: Proc. Amer. Math. Soc. 111 (1991), 403-411
MSC: Primary 30C50; Secondary 30C55
DOI: https://doi.org/10.1090/S0002-9939-1991-1037204-8
MathSciNet review: 1037204
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ S$ of normalized univalent functions. This is applied to the coefficient problem of $ {[f(z)]^\lambda },0 < \lambda < 1$ as well as to the problem of univalence of sections of the power series expansion of $ f(z)$.


References [Enhancements On Off] (What's this?)

  • [1] D. Bshouty and W. Hengartner, Local behaviour of coefficients in subclasses of S, Contemp. Math. Amer. Math. Soc. 38 (1985), 77-84. MR 789448
  • [2] -, A variation of the Koebe mapping in a dense subset of S, Canad. J. Math. 39 (1987), 54-73. MR 889106 (88j:30048)
  • [3] P. L. Duren, Univalent functions, Springer-Verlag, 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), 58-64. MR 697766 (85a:30030)
  • [5] A. Z. Grinshpan and I. M. Milin, Logarithmic coefficients means of univalent functions, Complex Variables Theory Appl. 7 (1986), 139-147. MR 877659 (88d:30022)
  • [6] W. K. Hayman and J. A. Hummel, Coefficients of powers of univalent functions, Complex Variables Theory Appl. 7 (1986), 51-70. MR 877651 (88d:30020)
  • [7] M. S. Robertson, The partial sums of multivalently starlike functions, Ann. of Math. 42 (1941), 829-838. MR 0004905 (3:79b)
  • [8] C. Schaeffer and D. C. Spencer, Coefficients of Schlicht functions, Duke Math. J. 10 (1943), 611-635. MR 0009631 (5:175i)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C50, 30C55

Retrieve articles in all journals with MSC: 30C50, 30C55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1037204-8
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society