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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2005 | 86 | 1 | 1-13

## Univalence, strong starlikeness and integral transforms

EN

### Abstrakty

EN
Let 𝓐 represent the class of all normalized analytic functions f in the unit disc Δ. In the present work, we first obtain a necessary condition for convex functions in Δ. Conditions are established for a certain combination of functions to be starlike or convex in Δ. 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 μ so that the non-linear integral transform $∫_0^z (ζ/f(ζ))^{μ} dζ$ is univalent in Δ. Finally, we give sufficient conditions for functions to be strongly starlike of order α.

1-13

wydano
2005

### Twórcy

autor
• Department of Mathematics, Faculty of Technology and Metallurgy, 4 Karnegijeva St., 11000 Belgrad, Serbia and Montenegro
autor
• Department of Mathematics, Indian Institute of Technology, Madras, Chennai-600 036, India
autor
• Department of Mathematics, Indian Institute of Technology, Madras, Chennai-600 036, India