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The region of values of the system {c 2, c 3, f(z 1), f′(z 1)} in the class of typically real functions

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The paper studies the region of values of the system {c 2, c 3, f(z 1), f′(z 1)},where z 1 is an arbitrary fixed point of the disk |z| < 1; f ∈ T,and the class T consists of all the functions f(z) = z + c 2 z 2 + c 3z3 + ⋯ regular in the disk |z| < 1 that satisfy the condition Im z · Im f(z) > 0 for Im z ≠ 0. The region of values of f′(z 1) in the subclass of functions f ∈ T with prescribed values c 2, c 3, and f(z 1) is determined. Bibliography: 10 titles.

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References

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia

    E. G. Goluzina

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  1. E. G. Goluzina
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Correspondence to E. G. Goluzina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 382, 2010, pp. 5–14.

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Goluzina, E.G. The region of values of the system {c 2, c 3, f(z 1), f′(z 1)} in the class of typically real functions. J Math Sci 176, 1–6 (2011). https://doi.org/10.1007/s10958-011-0385-8

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