Rocky Mountain Journal of Mathematics

Starlikeness of sections of univalent functions

M. Obradović and S. Ponnusamy

Full-text: Open access


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

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

First available in Project Euclid: 28 September 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Coefficient inequality analytic Hadamard convolution univalent and starlike functions


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.

Export citation


  • L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152.
  • D. Bshouty and W. Hengartner, Criteria for the extremality of the Koebe mapping, Proc. Amer. Math. Soc. 111 (1991), 403-411.
  • P.L. Duren, Univalent functions, Grundl. Math. Wissen. \bf259, Springer-Verlag, New York, 1983.
  • A.W. Goodman, Univalent functions, Volumes I and II, Mariner Publishing Co., Tampa, Florida, 1983.
  • J.A. Jenkins, On an inequality of Goluzin, Amer. J. Math. 73 (1951), 181-185.
  • M. Obradović and S. Ponnusamy, Partial sums and radius problem for certain class of conformal mappings, Sib. Mat. Zh. \bf52 (2011), 371-384 (in Russian); Sib. Math. J. \bf52 (2011), 291–302 (in English).
  • D.V. Prokhorov, Bounded univalent functions. Handbook of complex analysis: Geometric function theory, Volume 1, Kühnau, ed., Elsevier, Amsterdam, 2005.
  • M.S. Robertson, On the theory of univalent functions, Ann. Math. 37 (1936), 374-408.
  • –––, The partial sums of multivalently star-like functions, Ann. Math. 42 (1941), 829-838.
  • St. Ruscheweyh, On the radius of univalence of the partial sums of convex functions, Bull. Lond. Math. Soc. 4 (1972), 367-369.
  • T. Sheil-Small, A note on the partial sums of convex schlicht functions, Bull. Lond. Math. Soc. 2 (1970), 165-168.
  • G. Szegö, Zur Theorie der schlichten Abbildungen, Ann. Math. 100 (1928), 188-211. \noindentstyle