Z. Nehari found sufficient conditions implying univalence of analytic functions, expressed in terms of the Schwarzian derivative. His theorem had been used by us to generate additional families of conditions for univalence, depending on parameters.
Recently, Aliaga and Tuneski used the method of selecting parameters to find a new criterion for univalence of analytic functions. However, they presented determining specific suitable values of the parameters and their precise domain of admissibility for this family as an open question.
In what follows we obtain additional information about the exact domain of possible parameters in the family of criteria studied by Aliaga and Tuneski.
Univalent functions Univalence criteria
Mathematics Subject Classification
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Aliaga, E., Tuneski, N.: On existence of sufficient condition for univalence depending on two parameters. In: Proceedings of the V Congress of Mathematicians of Macedonia, vol. 2, pp. 5–9 (2015)Google Scholar
Aliaga, E., Tuneski, N.: The Schwarzian derivative as a condition for univalence. Adv. Math. Sci. J. 5, 111–116 (2016)MATHGoogle Scholar