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

Author： Goluzina E.  

Publisher： Springer Publishing Company

ISSN： 1072-3374

Source： Journal of Mathematical Sciences, Vol.176, Iss.1, 2011-07, pp. : 1-6

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Abstract

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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