Zalcman and generalized Zalcman conjecture for the class U

2020/05/28 by Obradović, Milutin, Tuneski, Nikola
#30C45 #30C50 #30C55 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.14301

Abstract

Function f(z)=z+∑_n=2^∞ a_n zⁿ, normalized, analytic and univalent in the unit disk \mathbb D=\z:|z|<1\, belongs to the class U. if, and only if, | ((z)/(f(z)))² -1|lt;1 (z∈ \mathbb D). In this paper, we prove the Zalcman and the generalized Zalcman conjecture for the class U and some values of parameters in the conjectures.

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