# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Univalence, strong starlikeness and integral transforms

### Tom 86 / 2005

Annales Polonici Mathematici 86 (2005), 1-13 MSC: 30C45, 30C55. DOI: 10.4064/ap86-1-1

#### Streszczenie

Let $\mathcal A$ represent the class of all normalized analytic functions $f$ in the unit disc ${\mit\Delta}$. In the present work, we first obtain a necessary condition for convex functions in ${\mit\Delta}$. Conditions are established for a certain combination of functions to be starlike or convex in ${\mit\Delta}$. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on $f$ and $\mu$ so that the non-linear integral transform $\int_0^z ({\zeta}/{f(\zeta)})^{\mu}\,d\zeta$ is univalent in ${\mit\Delta}$. Finally, we give sufficient conditions for functions to be strongly starlike of order $\alpha$.

#### Autorzy

Faculty of Technology and Metallurgy
4 Karnegijeva St.
Serbia and Montenegro
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• S. PonnusamyDepartment of Mathematics
Indian Institute of Technology
Chennai-600 036, India
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