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Title: Some properties of the class $\mathcal{U}$
Authors: Milutin Obradovic
Nikola Tuneski
Keywords: Mathematics - Complex Variables
Mathematics - Complex Variables
30C45, 30C50, 30C55
Issue Date: 20-Dec-2018
Abstract: In this paper we study the class $\mathcal{U}$ 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 \[\left|\left [\frac{z}{f(z)} \right]^{2}f'(z)-1 \right|<1\quad\quad (z\in {\mathbb D}).\] For functions in the class $\mathcal{U}$ we give sharp estimate of the second ant the third Hankel determinant, its relationship with the class of $\alpha$-convex functions, as well as certain starlike properties.
Appears in Collections:Faculty of Mechanical Engineering: Journal Articles

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