Subclasses of typically real functions determined by some modular inequalities
Leopold Koczan, Katarzyna Trąbka-Więcław (2010)
Annales UMCS, Mathematica
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Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ := {z ∈ C : |z| < 1}, normalized by f(0) = f'(0) - 1 = 0 and such that Im z Im f(z) ≥ 0 for z ∈ Δ. Moreover, let us denote: T(2) := {f ∈ T : f(z) = -f(-z) for z ∈ Δ} and TM, g := {f ∈ T : f ≺ Mg in Δ}, where M > 1, g ∈ T ∩ S and S consists of all analytic functions, normalized and univalent in Δ.We investigate classes in which the subordination is replaced with the majorization...