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

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The paper studies the region of values of the system {f(z 1), f(z 2), c 2},where z j , j=1, 2, are arbitrary fixed points of the disk |z|<1; f ∈ T, and the class T consists of all functions f(z) = z + c 2 z 2 + ··· regular in the disk |z| < 1 and satisfying the condition Im f(z)·Im z>0 for Im z > 0 for Im z ≠ 0. The region of values of f(z 1) in the subclass of functions f (z) ∈ T with prescribed values c 2 and f(z 2) is determined. Bibliography: 8 titles.

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References

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  1. St. Petersburg Department of the Steklov Mathematical Institute, 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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Dedicated to the 80th anniversary of I. P. Mityuk's birthday

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 7–17.

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Goluzina, E.G. The region of values of the system {c 2, f(z 1), f(z 2)} in the class of typically real functions. J Math Sci 166, 128–133 (2010). https://doi.org/10.1007/s10958-010-9852-x

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