Some properties of the class \(\mathcal{U}\)

Milutin Obradovic, Nikola Tuneski

Abstract


In this paper we study the class \(\mathcal{U}\) of functions that are analytic in the open unit disk \(D =\{z : |z| < 1\}\), normalized such that\(f(0) = f'(0)-1 = 0\) and satisfy \[\left|\left[\frac{z}{f(z)}\right]^2f'(z) - 1\right|< 1\quad  (z\in D).\]
For functions in the class \(\mathcal{U}\) we give sharp estimates of the second and the third Hankel determinant, its relationship with the class of \(\alpha\)-convex functions, as well as certain starlike properties.


Keywords


Analytic; class \(\mathcal{U}\); starlike, \(\alpha\)-convex; Hankel determinant

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References


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DOI: http://dx.doi.org/10.17951/a.2019.73.1.49-56
Date of publication: 2019-12-19 10:33:48
Date of submission: 2019-12-17 11:23:36


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