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On an estimate in the class of typically real functions

Let T(c2, c 3) be the class of functions \( f(z)=z+\sum\limits_{n=2}^{\infty } {{c_n}{z^n}} \) regular and typically real in the disk |z| < 1 with fixed values of the coefficients c 2 and c 3. The boundary functions of the region of values of f (z 0) (0 < |z0| < 1) and sharp estimates for f (r), 0 < r < 1, in the class T(c 2, c 3) are determined. Bibliography: 6 titles.


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Correspondence to E. G. Goluzina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 75–82.

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Goluzina, E.G. On an estimate in the class of typically real functions. J Math Sci 193, 40–44 (2013).

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  • Real Function
  • Boundary Function
  • Sharp Estimate