Coefficient inequalities for univalent starlike functions

Rok, strany: 2013, 1113 - 1122

Let ${\mathcal A}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$. In this paper the authors discuss necessary and sufficient coefficient conditions for $f\in {\mathcal A}$ of the form

$$ (((z) / (f(z))))^μ=1+b₁z+b₂z²+… $$

to be starlike in $\ID$ and more generally, starlike of some order $β$, $0≤ β <1$. Here $μ$ is a suitable complex number so that the right hand side expression is analytic in $\ID$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order $β$ is open.

ISO 690:

Obradović, M., Ponnusamy, S. 2013. Coefficient inequalities for univalent starlike functions. In Mathematica Slovaca, vol. 63, no.5, pp. 1113-1122. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0159-5

APA:

Obradović, M., Ponnusamy, S. (2013). Coefficient inequalities for univalent starlike functions. Mathematica Slovaca, 63(5), 1113-1122. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0159-5