Univalence, strong starlikeness and integral transforms

• Autorzy: M. Obradović , S. Ponnusamy , P. Vasundhra
• Języki publikacji: 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.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C55: General theory of univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 86
• Numer: 1
• Strony: 1-13

Daty

wydano

2005

Twórcy

autor

M. Obradović

• Department of Mathematics, Faculty of Technology and Metallurgy, 4 Karnegijeva St., 11000 Belgrad, Serbia and Montenegro

autor

S. Ponnusamy

• Department of Mathematics, Indian Institute of Technology, Madras, Chennai-600 036, India

autor

P. Vasundhra

• Department of Mathematics, Indian Institute of Technology, Madras, Chennai-600 036, India

Identyfikatory

DOI

10.4064/ap86-1-1