Some properties of the class U

2018/12/20 by Obradovic, Milutin, Tuneski, Nikola · 1 citation
#30C45 #30C50 #30C55 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.08503

Abstract

In this paper we study the class U of functions that are analytic in the open unit disk \mathbb D=\z:|z|<1\, normalized such that f(0)=f'(0)-1=0 and satisfy | [(z)/(f(z)) ]²f'(z)-1 |lt;1 (z∈ \mathbb D). For functions in the class U we give sharp estimate of the second ant the third Hankel determinant, its relationship with the class of α-convex functions, as well as certain starlike properties.

Cited by

• Symmetric Toeplitz determinants of some classes of univalent functions

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• Relations of the class U(λ) to other families of functions
• Hankel determinant of second order for some classes of analytic\n functions
• On relations between the classes \mathcal S and \mathcal U
• Two types of the second Hankel determinant for the class U and the general class S