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

Article

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; fT,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 fT with prescribed values c 2, c 3, and f(z 1) is determined. Bibliography: 10 titles.

Keywords

Russia Real Function Mathematical Institute Steklov Mathematical Institute Typically Real 
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References

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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