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On a region of values in the class of typically real functions

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Abstract

The paper studies the regions of values of the systems {f(z1), f(r1), f(r2),…, f(rn)} and {f(r1), f(r2),…, f (rn)}, where n ⁥ 2; z1 is an arbitrary fixed point of the disk U = {z: |z| < 1} with Im z1 ≠ 0; rj are fixed numbers, 0 < rj < 1, j = 1, 2,…, n; f ∈ T, and the class T consists of the functions f(z), f(0) = 0, f′(0) = 1, regular in the disk U and satisfying the condition Im f(z) · Imz > 0 for Im z ≠ 0. As an implication, the region of values of f(z1) in the subclass of functions f ∈ T with prescribed values f(rj) (j = 1, 2,…, n) is determined. Bibliography: 12 titles.

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References

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Authors and Affiliations

  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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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 5–16.

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Goluzina, E.G. On a region of values in the class of typically real functions. J Math Sci 150, 2005–2012 (2008). https://doi.org/10.1007/s10958-008-0116-y

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  • DOI: https://doi.org/10.1007/s10958-008-0116-y

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