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Functions whose derivative has positive real part


Author: R. R. London
Journal: Proc. Amer. Math. Soc. 103 (1988), 521-524
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1988-0943078-3
MathSciNet review: 943078
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Abstract: In this paper we find a sharp upper bound for $ \left\vert {z\,f'\left( z \right) / f\left( z \right)} \right\vert$, where $ f$ is a normalised analytic function with Re $ f'\left( z \right) > 0$ in the unit disc.


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

  • [1] P. L. Duren, Univalent functions, Springer-Verlag, Berlin and New York, 1983. MR 708494 (85j:30034)
  • [2] S. Ruscheweyh, Nichtlineare Extremalprobleme für holomorphe Stieltjesintegrale, Math. Z. 142 (1975), 19-23. MR 0374406 (51:10606)
  • [3] D. K. Thomas, On functions whose derivative has positive real part, Proc. Amer. Math. Soc. 98 (1986), 68-70. MR 848877 (87k:30064)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0943078-3
Article copyright: © Copyright 1988 American Mathematical Society

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