Rocky Mountain Journal of Mathematics

Starlikeness of sections of univalent functions

M. Obradović and S. Ponnusamy

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Abstract

Let ${\S}$ be the class of all normalized analytic and univalent functions in the unit disk $\ID$. In this paper, we determine condition so that each section $s_{n}(f,z)$ of $f\in {\S}$ is starlike in the disk $|z|\lt r_n$. In particular, $s_{n}(f,z)$ is starlike in $|z|\leq 1/2$ for $n \geq 47$.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 3 (2014), 1003-1014.

Dates
First available in Project Euclid: 28 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1411945676

Digital Object Identifier
doi:10.1216/RMJ-2014-44-3-1003

Mathematical Reviews number (MathSciNet)
MR3264494

Zentralblatt MATH identifier
1298.30012

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
Coefficient inequality analytic Hadamard convolution univalent and starlike functions

Citation

Obradović, M.; Ponnusamy, S. Starlikeness of sections of univalent functions. Rocky Mountain J. Math. 44 (2014), no. 3, 1003--1014. doi:10.1216/RMJ-2014-44-3-1003. https://projecteuclid.org/euclid.rmjm/1411945676


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