The region of values of the system {c2, f(z1), f(z2)} in the class of typically real functions

The paper studies the region of values of the system {f(z1), f(z2), c2}, where zj, j = 1, 2, are arbitrary fixed points of the disk {pipe}z{pipe}<1; f ∈ T, and the class T consists of all functions f(z) = z + c2z2 +... regular in the disk {pipe}z{pipe} < 1 and satisfying the condition Im f(z)·Im z>0 for Im z ≠ 0. The region of values of f(z1) in the subclass of functions f (z) ∈ T with prescribed values c2 and f(z2) is determined. Bibliography: 8 titles. © 2010 Springer Science+Business Media, Inc.